Talk:Geometric progression

message: Can common ratio's be imaginary? Maybe we should include that since the article specifically says they can be negative.  —Preceding unsigned comment added by 72.229.188.248 (talk) 02:34, 28 January 2011 (UTC)
thread_title:  A question 

message: I don't really agree with the paragaph:
:One cannot see why the proportion called arithmetical is any more arithmetical than that which is called geometrical, nor why the latter is more geometrical than the former. On the contrary, the primitive idea of geometrical proportion is based on arithmetic, for the notion of ratios springs essentially from the consideration of numbers 
That seems a rationalisation based on number, but it is not certain that mathematics started as number.
:It is "not certain" that it did?  Indeed, isn't it certain that it did not?  The notion of real number grew out of geometry!
For example, take a square, double the length of its sides, double again, and again.  Clearly the side lengths are in geometric progression; so too are the areas.  Take a different square, add 2 to the length of the sides (2 what?), add 2 again, and again.  This time the side lengths are in arithmetic progression, but the areas are not.  It seems natural to call the former geometric, leaving arithmetic to the latter.  In the medieval quadrivium, arithmetic was pure number, geometry was number in space, music number in time, and astronomy number in space and time; but I doubt that was the order in pre-history.--Henrygb 13:13, 21 Mar 2004 (UTC)
thread_title:  Paragraph problem 

message: The example for return on capital interest is not correct and misleading. Interest rates are calculated using compound interest rates. If one could get $16000 out of $2000 in 6 years, that would be quite awesome. I am not familiar with wikipedia to fix this example, thanks for taking note of it.
--Vastinnocentaims 15:20, 16 August 2005 (UTC)
thread_title:  Interest Rate bad example 

message: It's been a few years since I studied this subject, so I came on here to help myself solve a little problem I was having, and found that this article was of little help. Can someone please clarify the geometric series part of the article? What is X? I can tell X^n is the Nth term of the geometric sequence, but what is X? Maybe put an example in?--149.135.21.11 14:33, 13 March 2006 (UTC)
thread_title:  Clarification please? 

message: :a_n = a\,r^{n-1} \quad \mbox{where n is an integer such that }n \ge 1
In the case of the above, would it not be more elegant to say "n\in\mathbb{N}" in place of "\mbox{where n is an integer such that }n \ge 1"?
I'd change it myself, but I wouldn't want to mess around with something if there's a specific reason for that form. --MightyPenguin 11:53, 20 March 2006
:\mathbb{N} can contain zero, depending on the circumstances (see natural number).  As it's slightly ambiguous, it's probably better to leave it as is. siafu 21:44, 2 May 2006 (UTC)
thread_title: Notation

message: Who is to be given credit for discovering the geometric series simplification?  Gauss? 131.120.10.130 19:34, 19 July 2006 (UTC)
thread_title:  Credit for Series Simplification 

message: Why is there a constant factor "a" in all of these formulae?  Isn't it more concise to just say \sum_{k=0}^\infty r^k = \frac{1}{1-r} instead of :\sum_{k=0}^\infty ar^k = \frac{a}{1-r} ? Dougthebug 23:36, 5 February 2007 (UTC)
replies: text: The a is there because the definition of geometric progression does not assume that it starts with 1. It's probably simpler to just keep the a than to keep having to explain why it was taken out.--RDBury (talk) 13:20, 1 October 2009 (UTC)

text: The article deals with geometric series in general. I cannot see any good reason for giving anything less than the most general formulas. It is true that it is easy to derive the general formulas from more specific ones, but why is that a justification for not giving the formulas in their most general form? JamesBWatson (talk) 18:49, 4 October 2009 (UTC)

text: In addition to the above math-based reasons to retain the a, here's a encylcopedia-based suggestion:  discussion of these series is taught in high school with the constant a (sometimes at least).  So retaining the a makes the page more useful to readers with that level of experience.  Citations for the assertion about math teaching include the "Kaplan SAT Subject Test Mathematics Level 2" 2010(?) edition.  The constant was included in my daughter's high school classes, although that hardly qualifies as a decent citation. DavidHolmes0 (talk) 21:35, 6 September 2010 (UTC)
thread_title:  Constant Factor 

message: # Positive, the terms will all be the same sign as the initial term.
# Negative, the terms will alternate between positive and negative.
# Greater than 1, there will be exponential growth towards positive infinity.
I think that the third line should read:
Greater than 1, there will be exponential growth towards infinity (of the same sign as the first term).
eg, -1, -2, -4, -8 ....
common ratio is 2, and is > 1
This is only the second 'post' I have made to Wikipedia.  I would rather put this as a discussion item than wade in and edit the main page.
If someone with more experience agrees, would they please alter the main page.
Thank you
Jsryork 11:21, 7 May 2007 (UTC)
thread_title:  incorrect description of final outcome in one case 

message: Why is a needed in all these formulae? It's clear that it's a constant and therefore it can always come out of the summation... 83.67.217.254 20:41, 21 August 2007 (UTC)
replies: text: It can come out of the summation when you're solving for the sum of the series, but it's needed when expressing the series as "a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number". If you didn't have a factor of a in each term, you could only express geometric series for which the first term is 1. —David Eppstein 05:09, 27 August 2007 (UTC)
replies: text:  That is not a property of the series. Its an application not an algebraic property. This is clutter.  — Preceding unsigned comment added by 95.176.83.179 (talk) 10:37, 29 May 2011 (UTC)
replies: text:  Although not a significant improvement, it does allow the sum to be determined for an arbitrary geometric progression, not just one starting with "1", per David Eppstein's comment above.  — Arthur Rubin  (talk) 14:43, 29 May 2011 (UTC)
thread_title:  What's the purpose of "''a''" in all these formulae? 

message: 1) This page has several discrepancies in numbering of terms:
"Elementary properties" says a_n = a *r^(n-1)
i.e. terms start from n=1
 
however the summation formula and everything from the section "Geometric series" onwards uses:
a_k = ar^k starting with k=0
2) The term-index used varies between n, k and even i
Please use one consistent notation and one term-index throughout; most people would favor the notation a_k = ar^k (i.e. numbering always starts from 0) and index k for simplicity. It also keeps the summation formula simpler.  
Smcinerney 04:08, 3 September 2007 (UTC)
replies: text: I have revised the Elementary Properties section to be consistent with the Series section. Journeyman (talk) 23:18, 26 March 2008 (UTC)
thread_title:  Discrepancies in term numbering in formulae 

message: Hi, I just added an article entirely on the subject of infinite geometric series.  Geometric progressions and geometric series are important enough that they deserve separate articles. Jim 21:06, 22 September 2007 (UTC)
thread_title:  Geometric series article 

message: I had an assignment involving infinite geometric series and at the time I couldn't understand the justification for the formula presented here, as it looked like half of the formula just dissapeared. Later I found that it was because the r^infinity equalled zero. I tried to simplify this line of math so that others wouldn't be as confused as I was... is it mathematically correct tho, ne comments Laubpatr (talk) 04:34, 16 March 2008 (UTC)
replies: text: The argument you give is not quite correct, since r∞ is not well-defined.  However, it is true that if |r| < 1, then the value of rn can be made arbitrarily close to zero by selecting a sufficiently large value of n, that is, limn→∞ rn = 0. Michael Slone (talk) 08:23, 16 March 2008 (UTC)
thread_title:  Infinite Series Explained

message: The formula ar^(n-1) is easily derived and simplifies understanding. As my edits are always deleted by some insane, wide eyed, fool of a moderater I sha'n't waste my time producing one. But a derivation would be a worthy addition to the page.
Also a simple example would make this more accessable. Perhaps using the forumula to calculate compound interest.
Also, where are the link to the exponential function and the derivation of e? 
Page needs a lot of work.  —Preceding unsigned comment added by 91.111.137.74 (talk) 13:49, 16 August 2009 (UTC)
thread_title:  derivation and simple example 

message: The introduction of the article currently says that the ratio between adjacent terms is "equal to the sequence's start value".  That doesn't make sense to me, since I don't know what is meant by progression's start value.  Perhaps the use of that phrase is a remnant from an earlier edition of the page wherein the constant "a" was not used?
In any case, can someone can clarify the phrase in the article, or remove it?
I know I'm supposed to Be Bold in editing, so maybe I should have removed the phrase, but this would have been my first edit to an article, and leading from ignorance was unappealing.  Helpful suggestions are welcome.
DavidHolmes0 (talk) 21:52, 6 September 2010 (UTC)
replies: text: Please ignore my comments above, which, on later reading, don't seem to match the history of the article.  What was I thinking?  DavidHolmes0 (talk) 15:02, 21 September 2010 (UTC)
thread_title:  start value?  whazzat? 

message: Under the Geometric Series heading there is a line that says, "Differentiating this formula with respect to r allows us to arrive at formulae for sums of the form." This is a tad bit confusing because it is first unclear which formula "this formula" is.  Apart from simply editing for clarity, should this material be moved to a section about calculus? Thelema418 (talk) 05:25, 23 August 2012 (UTC)
thread_title:  Calculus on Geometric Series 

message: I propose that Geometric progression be merged in part or whole into Geometric series. The concept of the progression or sequence is necessary to understand the series, so it is necessary in the Series article.  For some reason, the series article concerns infinite series, but finite series are described in the geometric progression article.  This is confusing because it makes it sound as though Geometric series refers to the infinite progression, and never a finite sequence. Thelema418 (talk) 02:20, 24 August 2012 (UTC)
replies: text: I would agree; they should be together as are Arithmetic Progression and Arithmetic Series. It's confusing to have Geometric Progression and Geometric Series as separate, lengthy articles. Startswithj (talk) 18:48, 30 November 2013 (UTC)

text: I disagree with the merger proposal.  See my comments on :Talk:Geometric series#Merger proposal. Jim.belk (talk) 05:02, 26 January 2014 (UTC)

text: I also disagree. A progression and a serie are totally differents objects. As far as the merged proposal is concerned: both progression and series are infinite, which do not forbid to look at finite inital sub-series. 2A02:1205:C6B7:F9C0:8150:27F3:EB3E:54DC (talk) 17:19, 22 July 2014 (UTC)

text: Agree. See my comments in Talk:Geometric series#Merger proposal. Mario Castelán Castro (talk) 00:52, 8 February 2015 (UTC)
thread_title:  Merger proposal 

message: Is it possible to find R given the sum, first term, and number of terms? 
I've asked my math teachers this and they all said no. I'm assuming that the responses here will be the same, but even if it's not possible, how close can I get to finding the answer?  — Preceding unsigned comment added by 71.206.163.33 (talk) 21:22, 25 August 2013 (UTC)
replies: text: In a sense, yes, if r is positive.  S(a,r,n) is an increasing function of r for r nonnegative, so there is a unique solution of S(a,r,n)=S given a, n, and S if S > a.  However, there isn't a "closed form" solution.  — Arthur Rubin  (talk) 01:03, 27 November 2013 (UTC)
thread_title:  Finding R 

message: I notice that 
the product equal to P=(a0*a1)^((n+1)/2)
The correct formula should be P=(a0*a1)^(n/2)
:No, the formula given, P = (a_0 a_n)^\frac{n+1}{2}, is correct. There are n + 1 terms since the first term is indexed by "0", and the proof is straight-forward. Bill Cherowitzo  (talk) 18:48, 24 April 2015 (UTC)
thread_title:  An error in product section 

message: Epp's discrete math book and Rosen's discrete math book place no restrictions on a and r. Since the sequences are defined using multiplication the restrictions are unnecessary. Occam's razor dictates that the restrictions be omitted. 68.81.2.180 (talk) 18:37, 25 May 2022 (UTC)
thread_title:  dubious restrictions on a and r 

message: The given formula for the product of the first n elements obviously does not hold if a<0: For example, with a=-1, n=0 and r=1, the product formula yields -1 = 1. I cannot find any hint on additional constraints for a in the article, though. 2A02:908:3220:960:7488:8916:ED75:DE65 (talk) 10:55, 22 January 2024 (UTC)
thread_title:  Problem with product formula