【数理考古学】オイラー定数(Eulerian Constant)の求め方

それにつけても**ベルヌーイ**や**オイラー**の名前を冠した式や定数の数には驚かされます。しかも**ベルヌーイ**が一族名なのに対して**オイラー**は個人名なのです。もしかしたら**ブルバキ**みたいに集団ペンネームだったのでは？
[ニコラ・ブルバキ - Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%8B%E3%82%B3%E3%83%A9%E3%83%BB%E3%83%96%E3%83%AB%E3%83%90%E3%82%AD)
著名なのはこの辺り。
[ベルヌーイ数とベルヌーイ多項式](https://shadowacademy.web.fc2.com/bernoulli.html)
[ベルヌーイ数の応用―テイラー展開―](https://shadowacademy.web.fc2.com/bernoullitaylor.html)

>①**頂点**(<font color=blue>Vertex</font>)の数を<font color=purple>V</font>、**辺**(<font color=blue>Edge</font>)の数を<font color=purple>E</font>、**面**(<font color=blue>Face</font>)の数を<font color=purple>F</font>としたとき、**凸多面体**に対し、
<font color=purple>χ</font>≡<font color=purple>V－E＋F</font>＝<font color=green>2</font>
が成り立ち、これを「**オイラーの多面体定理**(<font color=blue>Eulerian Polyhedral Theorem</font>)」と呼ぶが、このとき、<font color=purple>χ</font>は「**オイラー標数**(<font color=blue>Eulerian Characteristic</font>)」と呼ばれる。

>②また、
<font color=purple>γ</font> ≡ <font color=purple>lim</font>(<font color=blue>n→∞</font>) (<font color=purple>1＋1/2＋1/3＋…＋1/n-log(n)</font>)＝<font color=green>0.5772156649…</font>
は、「**オイラー定数**(<font color=blue>Eulerian Constant</font>)」、あるいは「**オイラー・マスケローニ定数**(<font color=blue>Euler-Mascheroni Constant</font>)」と呼ばれている。

このうち「**オイラー標数**(<font color=blue>Eulerian Characteristic</font>)」については下記の投稿で扱いました。
[【オイラーの多面体定理と正多面体】とある「球面幾何学」の出発点…](https://qiita.com/ochimusha01/items/5f8dbf33bac5b7227a11)

* 立体上における**オイラー標数**=<font color=green>2</font>は「**偶数系立体**(<font color=blue>Even-numbered Solid</font>)=**正多面体**(<font color=blue>Platonic solid=プラトン立体</font>)でいうと**正六面体**(<font color=blue>Cube</font>),**正八面体**(<font color=blue>Regular Octahedron</font>),**正12面体**(<font color=blue>Regular Dodecahedron</font>),**正20面体**(<font color=blue>Regular Icosahedron</font>)」における(<font color=blue>凸型正多面体の場合は単一となるその立体の</font>)外接球面上の**対蹠**(<font color=blue>Antipodes</font>)の対、「**奇数系立体**(<font color=blue>Even-numbered Solid</font>)=**正多面体**でいうと**正四面体**(<font color=blue>Regular Tetrahedron</font>)」における(<font color=blue>それぞれの対蹠を始点とし、特定の面を終点とする展開の対における</font>)**始点と終面**に該当する。**オイラーの多面体定理**の証明を通じて得られるこのイメージは、関数における(<font color=blue>逆関数を持たない</font>)**偶関数**(<font color=blue>Even Function</font>)と(<font color=blue>常に逆関数と一対で現れる</font>)**奇関数**(<font color=blue>Odd Function</font>)の関係に対応する。<br>[オイラーの多面体定理の証明](https://mathtrain.jp/euler_poly)<br>[偶関数と奇関数の意味，性質などまとめ](https://mathtrain.jp/evenoddfunction)
* 一方、 平面上における**オイラー標数**=<font color=green>1</font>と線上における**オイラー標数**=<font color=green>0</font>は**多辺形**(<font color=blue>Polylateral</font>)/**多角形**(<font color=blue>Polygon</font>）の**面数**を<font color=green>表裏2面</font>と数えるか(<font color=blue>xyz座標系が実軸と認識される世界</font>)、<font color=green>片側1面</font>と数えるか(<font color=blue>xy座標系が実軸と認識される世界</font>)輪郭線のみに着目して<font color=green>0面</font>と数えるか(<font color=blue>数直線の様にスカラー量の増減のみが実軸と認識される世界</font>)に由来し、この選択こそがまさにそれぞれ<font color=purple>2.0-2,5次元</font>と<font color=purple>3.0-3.5次元</font>、<font color=purple>1.0-1,5次元</font>と<font color=purple>2.0-2.5次元</font>の境界線となる。<br>[オイラー数と曲面](http://www.med.nihon-u.ac.jp/home/sudagawa/%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E6%95%B0%E3%81%A8%E6%9B%B2%E9%9D%A2.pdf)<br>ちなみに(<font color=blue>線上もしくは平面上の</font>)**多角形**において**頂点数**と**辺数**は必ず等しくなるが、**オイラーの公式**(<font color=blue>Eulerian Formula</font>)<font color=purple>e^θi</font>=<font color=purple>cos(θ)+sin(θi)</font>など(<font color=blue>1の冪根に由来する</font>)**ガウスの巡回群**を用いた計算ではこれに(<font color=blue>始点と重なる終点、あるいは終点と重なる始点となる</font>)**原点**<font color=green>1</font>を加える。例えば統計言語Rにおける(<font color=blue>円の近似たる</font>)**60角形**の表現は`c<-seq(-pi,pi,length=61),x<-cos(c),y<-sin(c)`となる。<br>[1の冪根 - Wikipedia](https://ja.wikipedia.org/wiki/1%E3%81%AE%E5%86%AA%E6%A0%B9)<br>[【無限遠点を巡る数理】オイラーの公式と等比数列③Cos波とSin波の正体？](https://qiita.com/ochimusha01/items/9014922c8aeff3dd9670)

今回は「**オイラー定数**(<font color=blue>Eulerian Constant</font>)」の概念に挑戦してみたいと思います。

#オイラー定数(<font color=blue>Eulerian Constant</font>)の求め方

[オイラーの定数 γ について− いろいろな表現の仕方 −](http://chart.co.jp/subject/sugaku/suken_tsushin/74/74-7.pdf)
[オイラーの定数 - Wikipedia](https://ja.wikipedia.org/wiki/%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E3%81%AE%E5%AE%9A%E6%95%B0)

><font color=purple>lim</font>(<font color=blue>n=1→inf(inity)</font>)<font color=purple>sum(k=1→n)(1/k)</font>
>
>上式中の<font color=purple>sum部</font>は**調和級数**(<font color=blue>Harmonic Series</font>)と呼ばれる。**調和級数が発散する**という事実は、今日においては微分積分学の初歩であるが、古くは収束すると考えられていた。
>
>**調和級数**が発散することの証明を最初に行ったのは、<font color=green>14世紀</font>のパリ大学の**ニコル・オレーム**であるが、これには誤りがあり、正しい証明が得られたのは<font color=blue>17世紀</font>になってからである。その後**ライプニッツ**などは<font color=purple>有限項の調和級数の近似式</font>に関心をもつなど<font color=green>17世紀</font>においても数学的な関心を集めていた。
>[ニコル・オレーム - Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%8B%E3%82%B3%E3%83%AB%E3%83%BB%E3%82%AA%E3%83%AC%E3%83%BC%E3%83%A0)
>
><font color=purple>有限項の調和級数の近似式</font>への関心から、**レオンハルト・オイラー**は**調和級数**の増え方が極限において**対数関数**に等しいことを証明した。つまり、**調和級数**と**対数関数**との差はある定数に収束し、それがのちに**オイラーの定数**と呼ばれるようになった。**オイラー**はこの値を<font color=green>小数第6位</font>まで求めた。その後、**ロレンツォ・マスケローニ**が<font color=green>第32位</font>まで求め（<font color=blue>ただし、正しかったのは第20位まで</font>）<font color=purple>γ</font>の記号で表した。

**オイラー定数**は<font color=green>1/22</font>までの計算で**小数点下1桁目**<font color=green>5</font>、<font color=green>1/180</font>までの計算で**小数点下2桁目**<font color=green>7</font>が得られます。そもそもここまでが既に途方もない計算量なんですね。

```R
> 1-log(1)
[1] 1

> 1+1/2-log(2)
[1] 0.8068528

> 1+1/2+1/3-log(3)
[1] 0.734721

> 1+1/2+1/3+1/4-log(4)
[1] 0.697039

> 1+1/2+1/3+1/4+1/5-log(5)
[1] 0.6738954

> 1+1/2+1/3+1/4+1/5+1/6-log(6)
[1] 0.6582405

> 1+1/2+1/3+1/4+1/5+1/6+1/7-log(7)
[1] 0.646947

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8-log(8)
[1] 0.6384156

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9-log(9)
[1] 0.6317437

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10-log(10)
[1] 0.6263832

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11-log(11)
[1] 0.6219821

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12-log(12)
[1] 0.618304

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13-log(13)
[1] 0.6151844

 > 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14-log(14)
[1] 0.612505

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15-log(15)
[1] 0.6101788

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16-log(16)
[1] 0.6081403

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17-log(17)
[1] 0.6063392

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18-log(18)
[1] 0.6047363

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19-log(19)
[1] 0.6033007

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20-log(20)
[1] 0.6020074

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21-log(21)
[1] 0.6008363

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22-log(22)
[1] 0.5997708

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23-log(23)
[1] 0.5987973

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24-log(24)
[1] 0.5979043

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25-log(25)
[1] 0.5970824

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26-log(26)
[1] 0.5963232

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27-log(27)
[1] 0.5956199

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28-log(28)
[1] 0.5949665

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29-log(29)
[1] 0.594358

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30-log(30)
[1] 0.5937897

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31-log(31)
[1] 0.593258

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32-log(32)
[1] 0.5927593

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33-log(33)
[1] 0.5922907

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34-log(34)
[1] 0.5918495

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35-log(35)
[1] 0.5914334

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36-log(36)
[1] 0.5910403

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37-log(37)
[1] 0.5906683

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38-log(38)
[1] 0.5903159

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39-log(39)
[1] 0.5899814

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40-log(40)
[1] 0.5896636

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41-log(41)
[1] 0.5893612

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42-log(42)
[1] 0.5890732

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43-log(43)
[1] 0.5887985

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44-log(44)
[1] 0.5885363

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45-log(45)
[1] 0.5882856

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46-log(46)
[1] 0.5880458

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47-log(47)
[1] 0.5878162

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48-log(48)
[1] 0.5875962

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49-log(49)
[1] 0.587385

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50-log(50)
[1] 0.5871823

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51-log(51)
[1] 0.5869875

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52-log(52)
[1] 0.5868002

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53-log(53)
[1] 0.58662

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54-log(54)
[1] 0.5864463

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55-log(55)
[1] 0.586279

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56-log(56)
[1] 0.5861177

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57-log(57)
[1] 0.5859619

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58-log(58)
[1] 0.5858116

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59-log(59)
[1] 0.5856663

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60-log(60)
[1] 0.5855259

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61-log(61)
[1] 0.58539

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62-log(62)
[1] 0.5852585

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63-log(63)
[1] 0.5851312

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64-log(64)
[1] 0.5850078

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65-log(65)
[1] 0.5848882

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66-log(66)
[1] 0.5847723

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67-log(67)
[1] 0.5846598

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68-log(68)
[1] 0.5845506

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69-log(69)
[1] 0.5844445

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70-log(70)
[1] 0.5843415

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71-log(71)
[1] 0.5842414

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72-log(72)
[1] 0.584144

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73-log(73)
[1] 0.5840493

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74-log(74)
[1] 0.5839572

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75-log(75)
[1] 0.5838675

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76-log(76)
[1] 0.5837802

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77-log(77)
[1] 0.5836951

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78-log(78)
[1] 0.5836122

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79-log(79)
[1] 0.5835314

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80-log(80)
[1] 0.5834526

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81-log(81)
[1] 0.5833758

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82-log(82)
[1] 0.5833008

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83-log(83)
[1] 0.5832277

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84-log(84)
[1] 0.5831562

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85-log(85)
[1] 0.5830865

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86-log(86)
[1] 0.5830184

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87-log(87)
[1] 0.5829518

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88-log(88)
[1] 0.5828867

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89-log(89)
[1] 0.5828231

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90-log(90)
[1] 0.5827609

1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91-log(91)

[1] 0.5827001

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92-log(92)
[1] 0.5826406

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93-log(93)
[1] 0.5825824

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94-log(94)
[1] 0.5825254

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95-log(95)
[1] 0.5824696

1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96-log(96)

[1] 0.582415

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97-log(97)
[1] 0.5823614

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98-log(98)
[1] 0.582309

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99-log(99)
[1] 0.5822577

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100-log(100)
[1] 0.5822073

1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101-log(101)

 [1] 0.582158

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102-log(102)
[1] 0.5821096

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103-log(103)
[1] 0.5820622

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104-log(104)
[1] 0.5820157

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105-log(105)
[1] 0.58197

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106-log(106)
[1] 0.5819252

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107-log(107)
[1] 0.5818813

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108-log(108)
[1] 0.5818382

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109-log(109)
[1] 0.5817958

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110-log(110)
[1] 0.5817542

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111-log(111)
[1] 0.5817134

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112-log(112)
[1] 0.5816733

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113-log(113)
[1] 0.5816339

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114-log(114)
[1] 0.5815952

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115-log(115)
[1] 0.5815572

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116-log(116)
[1] 0.5815198

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117-log(117)
[1] 0.5814831

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118-log(118)
[1] 0.581447

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119-log(119)
[1] 0.5814115

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120-log(120)
[1] 0.5813765

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121-log(121)
[1] 0.5813422

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122-log(122)
[1] 0.5813084

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123-log(123)
[1] 0.5812752

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124-log(124)
[1] 0.5812425

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125-log(125)
[1] 0.5812103

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126-log(126)
[1] 0.5811787

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127-log(127)
[1] 0.5811475

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128-log(128)
[1] 0.5811168

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129-log(129)
[1] 0.5810866

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130-log(130)
[1] 0.5810569

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131-log(131)
[1] 0.5810276

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132-log(132)
[1] 0.5809988

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133-log(133)
[1] 0.5809704

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134-log(134)

[1] 0.5809424
> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135-log(135)
[1] 0.5809148

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136-log(136)
[1] 0.5808876

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137-log(137)
[1] 0.5808609

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138-log(138)
[1] 0.5808345

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139-log(139)
[1] 0.5808085

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140-log(140)
[1] 0.5807828

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141-log(141)
[1] 0.5807576

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142-log(142)
[1] 0.5807327

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143-log(143)
[1] 0.5807081

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144-log(144)
[1] 0.5806839

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145-log(145)
[1] 0.58066

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146-log(146)
[1] 0.5806364

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147-log(147)
[1] 0.5806132

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148-log(148)
[1] 0.5805902

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149-log(149)
[1] 0.5805676

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150-log(150)
[1] 0.5805453

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151-log(151)
[1] 0.5805233

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152-log(152)
[1] 0.5805015

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153-log(153)
[1] 0.5804801

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154-log(154)
[1] 0.5804589

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155-log(155)
[1] 0.580438

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156-log(156)
[1] 0.5804174

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157-log(157)
[1] 0.580397

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158-log(158)
[1] 0.5803769

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159-log(159)
[1] 0.580357

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160-log(160)
[1] 0.5803374

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161-log(161)
[1] 0.580318

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162-log(162)
[1] 0.5802989

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163-log(163)
[1] 0.58028

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164-log(164)
[1] 0.5802613

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165-log(165)
[1] 0.5802429

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166-log(166)
[1] 0.5802247

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167-log(167)
[1] 0.5802067

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168-log(168)
[1] 0.5801889

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169-log(169)
[1] 0.5801713

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170-log(170)
[1] 0.580154

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171-log(171)
[1] 0.5801368

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172-log(172)
[1] 0.5801198

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173-log(173)
[1] 0.5801031

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174-log(174)
[1] 0.5800865

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175-log(175)
[1] 0.5800701

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175+1/176-log(176)
[1] 0.5800539

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175+1/176+1/177-log(177)
[1] 0.5800379

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175+1/176+1/177+1/178-log(178)
[1] 0.580022

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175+1/176+1/177+1/178+1/179-log(179)
[1] 0.5800064

> 1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175+1/176+1/177+1/178+1/179+1/180-log(180)
[1] 0.5799909

1+1/2+1/3+1/4+1/5+1/6+1/7+1/8+1/9+1/10+1/11+1/12+1/13+1/14+1/15+1/16+1/17+1/18+1/19+1/20+1/21+1/22+1/23+1/24+1/25+1/26+1/27+1/28+1/29+1/30+1/31+1/32+1/33+1/34+1/35+1/36+1/37+1/38+1/39+1/40+1/41+1/42+1/43+1/44+1/45+1/46+1/47+1/48+1/49+1/50+1/51+1/52+1/53+1/54+1/55+1/56+1/57+1/58+1/59+1/60+1/61+1/62+1/63+1/64+1/65+1/66+1/67+1/68+1/69+1/70+1/71+1/72+1/73+1/74+1/75+1/76+1/77+1/78+1/79+1/80+1/81+1/82+1/83+1/84+1/85+1/86+1/87+1/88+1/89+1/90+1/91+1/92+1/93+1/94+1/95+1/96+1/97+1/98+1/99+1/100+1/101+1/102+1/103+1/104+1/105+1/106+1/107+1/108+1/109+1/110+1/111+1/112+1/113+1/114+1/115+1/116+1/117+1/118+1/119+1/120+1/121+1/122+1/123+1/124+1/125+1/126+1/127+1/128+1/129+1/130+1/131+1/132+1/133+1/134+1/135+1/136+1/137+1/138+1/139+1/140+1/141+1/142+1/143+1/144+1/145+1/146+1/147+1/148+1/149+1/150+1/151+1/152+1/153+1/154+1/155+1/156+1/157+1/158+1/159+1/160+1/161+1/162+1/163+1/164+1/165+1/166+1/167+1/168+1/169+1/170+1/171+1/172+1/173+1/174+1/175+1/176+1/177+1/178+1/179+1/180-log(180)
```
不勉強もあって、オイラーが**グレゴリー級数**(<font color=blue>Gregory Series</font>)の計算を加速させた**オイラー変換**(<font color=blue>Eulerian Transformation</font>)の様な画期的数理が発明されたという話を聞きません。オイラーもやはりこうした計算を愚直に繰り返したのでしょうか？
[【数理考古学】とある円周率への挑戦？](https://qiita.com/ochimusha01/items/5c8a62486ea4d5d1d73a)
![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/597772/38091f8a-9172-e17d-dffb-cedc085b38d8.png)

とはいえ流石にこのまま手計算式で続けるのには無理があるので、ここで<font color=purple>Reduce関数</font>を導入します。まさにこういう計算を行う為に設定された関数なんですね。上掲箇所までの再計算も一瞬で終わります。
[Reduce関数活用例：複利計算シミュレーション](https://qiita.com/stkdev/items/16099f6e35b98ae62389)
![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/597772/3ca00656-7d96-7d4b-222b-981f24a5f7cc.png)

```R
> cx=1:180
> cy1<-Reduce(function(a,b){a+1/b},cx,accumulate = T)
> cy1
[1] 1.000000 1.500000 1.833333 2.083333 2.283333 2.450000 2.592857 2.717857
[9] 2.828968 2.928968 3.019877 3.103211 3.180134 3.251562 3.318229 3.380729
[17] 3.439553 3.495108 3.547740 3.597740 3.645359 3.690813 3.734292 3.775958
[25] 3.815958 3.854420 3.891457 3.927171 3.961654 3.994987 4.027245 4.058495
[33] 4.088798 4.118210 4.146781 4.174559 4.201586 4.227902 4.253543 4.278543
[41] 4.302933 4.326743 4.349999 4.372726 4.394948 4.416687 4.437964 4.458797
[49] 4.479205 4.499205 4.518813 4.538044 4.556912 4.575430 4.593612 4.611469
[57] 4.629013 4.646255 4.663204 4.679870 4.696264 4.712393 4.728266 4.743891
[65] 4.759276 4.774427 4.789352 4.804058 4.818551 4.832837 4.846921 4.860810
[73] 4.874509 4.888022 4.901356 4.914514 4.927501 4.940321 4.952979 4.965479
[81] 4.977825 4.990020 5.002068 5.013973 5.025738 5.037366 5.048860 5.060224
[89] 5.071459 5.082571 5.093560 5.104429 5.115182 5.125820 5.136346 5.146763
[97] 5.157072 5.167277 5.177378 5.187378 5.197279 5.207082 5.216791 5.226407
[105] 5.235930 5.245364 5.254710 5.263969 5.273144 5.282235 5.291244 5.300172
[113] 5.309022 5.317794 5.326489 5.335110 5.343657 5.352132 5.360535 5.368868
[121] 5.377133 5.385329 5.393460 5.401524 5.409524 5.417461 5.425335 5.433147
[129] 5.440899 5.448591 5.456225 5.463801 5.471319 5.478782 5.486190 5.493543
[137] 5.500842 5.508088 5.515282 5.522425 5.529517 5.536560 5.543553 5.550497
[145] 5.557394 5.564243 5.571046 5.577803 5.584514 5.591181 5.597803 5.604382
[153] 5.610918 5.617412 5.623863 5.630273 5.636643 5.642972 5.649261 5.655511
[161] 5.661722 5.667895 5.674030 5.680128 5.686188 5.692212 5.698201 5.704153
[169] 5.710070 5.715952 5.721800 5.727614 5.733395 5.739142 5.744856 5.750538
[177] 5.756188 5.761806 5.767392 5.772948
> cy2<-cy1-log(cx)
> cy2
[1] 1.0000000 0.8068528 0.7347210 0.6970390 0.6738954 0.6582405 0.6469470
[8] 0.6384156 0.6317437 0.6263832 0.6219821 0.6183040 0.6151844 0.6125050
[15] 0.6101788 0.6081403 0.6063392 0.6047363 0.6033007 0.6020074 0.6008363
[22] 0.5997708 0.5987973 0.5979043 0.5970824 0.5963232 0.5956199 0.5949665
[29] 0.5943580 0.5937897 0.5932580 0.5927593 0.5922907 0.5918495 0.5914334
[36] 0.5910403 0.5906683 0.5903159 0.5899814 0.5896636 0.5893612 0.5890732
[43] 0.5887985 0.5885363 0.5882856 0.5880458 0.5878162 0.5875962 0.5873850
[50] 0.5871823 0.5869875 0.5868002 0.5866200 0.5864463 0.5862790 0.5861177
[57] 0.5859619 0.5858116 0.5856663 0.5855259 0.5853900 0.5852585 0.5851312
[64] 0.5850078 0.5848882 0.5847723 0.5846598 0.5845506 0.5844445 0.5843415
[71] 0.5842414 0.5841440 0.5840493 0.5839572 0.5838675 0.5837802 0.5836951
[78] 0.5836122 0.5835314 0.5834526 0.5833758 0.5833008 0.5832277 0.5831562
[85] 0.5830865 0.5830184 0.5829518 0.5828867 0.5828231 0.5827609 0.5827001
[92] 0.5826406 0.5825824 0.5825254 0.5824696 0.5824150 0.5823614 0.5823090
[99] 0.5822577 0.5822073 0.5821580 0.5821096 0.5820622 0.5820157 0.5819700
[106] 0.5819252 0.5818813 0.5818382 0.5817958 0.5817542 0.5817134 0.5816733
[113] 0.5816339 0.5815952 0.5815572 0.5815198 0.5814831 0.5814470 0.5814115
[120] 0.5813765 0.5813422 0.5813084 0.5812752 0.5812425 0.5812103 0.5811787
[127] 0.5811475 0.5811168 0.5810866 0.5810569 0.5810276 0.5809988 0.5809704
[134] 0.5809424 0.5809148 0.5808876 0.5808609 0.5808345 0.5808085 0.5807828
[141] 0.5807576 0.5807327 0.5807081 0.5806839 0.5806600 0.5806364 0.5806132
[148] 0.5805902 0.5805676 0.5805453 0.5805233 0.5805015 0.5804801 0.5804589
[155] 0.5804380 0.5804174 0.5803970 0.5803769 0.5803570 0.5803374 0.5803180
[162] 0.5802989 0.5802800 0.5802613 0.5802429 0.5802247 0.5802067 0.5801889
[169] 0.5801713 0.5801540 0.5801368 0.5801198 0.5801031 0.5800865 0.5800701
[176] 0.5800539 0.5800379 0.5800220 0.5800064 0.5799909

#グラフ化
plot(cx,cy1,type="l",xlim=c(1,180),ylim=c(0,6),main="Eulerian Constant",xlab="",ylab="",col=rgb(0,0,1))
par(new=T)#上書き指定
plot(log(cx),type="l",xlim=c(1,180),ylim=c(0,6),main="",xlab="",ylab="",col=rgb(1,0,0))
par(new=T)#上書き指定 
plot(cx,cy2,type="l",xlim=c(1,180),ylim=c(0,6),main="",xlab="",ylab="",col=rgb(0,1,0))
legend("bottomright", legend=c("Harmonic Series","Natural Logarithm","Eulerian Constant"),lty=c(1,1),col=c(rgb(0,0,1),rgb(1,0,0),rgb(0,1,0)))
```
**常用対数計算**の場合もそうですが、こういう場合に**コンピューター導入の威力**を感じます。というよりむしろ、こうした手間の掛かる計算の存在こそがコンピューター登場を促したとも。
[【数理考古学】常用対数表(Table of Common Logarithms)を使った計算](https://qiita.com/ochimusha01/items/b7ce3c7d86ab39263c68)

**小数点下3桁**<font color=green>7</font>が定まるのは<font color=green>1/638</font>以上、**小数点下4桁**<font color=green>2</font>が定まるのは<font color=green>1/5933</font>以上、**小数点下5桁**<font color=green>1</font>が定まるのは<font color=green>1/116684</font>以上、**小数点下6桁**<font color=green>5</font>が定まるのは<font color=green>1/1753777</font>以上となります。どうやって計算したのかまでは分かりませんがオイラーは<font color=green>18世紀</font>段階でここまでは計算した訳です。検算の手間も大変なものだった事でしょう。既に**調和級数が収束しない**事までは明らかだったとはいえ、良くぞここまで突き進めたものです。流石は「<font color=red>幾何学</font>（<font color=blue>学問</font>）<font color=red>に王道なし</font>」の名言を残しただけの人だけはあります。当時独特の**開拓者精神**の産物でもあった？

```R
#Eulerian Constant 0.5772156649…
ec <-function(x){
c0=1:x
c1<-Reduce(function(a,b){a+1/b},c0)
c1-log(x)
}

#小数点下3桁7が定まるのは1/638以上
> ec(637)
[1] 0.5780004
> ec(638)
[1] 0.5779992

#小数点下4桁2が定まるのは1/5933以上
> ec(5932)
[1] 0.5773
> ec(5933)
[1] 0.5772999

#小数点下5桁1が定まるのは1/116684以上
> ec(116683)
[1] 0.57722
> ec(116684)
[1] 0.5772199

#小数点下6桁5が定まるのは1/1753777以上
> ec(1753776)
[1] 0.577216
> ec(1753777)
[1] 0.5772159
```

これは少なくとも**明日をも知れぬ毎日を送ってる人間**が腰を据えて出来る計算ではありません。そういえば**エコール・ポリテクニーク**入学への望みを断たれ「<font color=red>僕にはもう時間がない</font>(<font color=blue>je n'ai pas le temps</font>)」と書き残して早世した**フランス人数学者**もいましたね。
[エコール・ポリテクニーク - Wikipedia](https://ja.wikipedia.org/wiki/%E3%82%A8%E3%82%B3%E3%83%BC%E3%83%AB%E3%83%BB%E3%83%9D%E3%83%AA%E3%83%86%E3%82%AF%E3%83%8B%E3%83%BC%E3%82%AF)
[エヴァリスト・ガロア - Wikipedia](https://ja.wikipedia.org/wiki/%E3%82%A8%E3%83%B4%E3%82%A1%E3%83%AA%E3%82%B9%E3%83%88%E3%83%BB%E3%82%AC%E3%83%AD%E3%82%A2)

近世数学が**ベルヌーイ家**の様な絶対君主の庇護を受けた名族、あるいはその引き立てによって世に出た**オイラー**の様な人物に牽引されてきたのには相応の理由があったのです。
[ベルヌーイ家 - Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%99%E3%83%AB%E3%83%8C%E3%83%BC%E3%82%A4%E5%AE%B6)
[レオンハルト・オイラー - Wikipedia](https://ja.wikipedia.org/wiki/%E3%83%AC%E3%82%AA%E3%83%B3%E3%83%8F%E3%83%AB%E3%83%88%E3%83%BB%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC)

そんな感じで以下続報…