Vanilla Ice-Cream

Vanilla ice-cream is the first flavour invented in the ice cream history. Before that, people were eating plain ice cream without any flavour. They simply blended the ice cream with sugar or anything they like. It was a great history on inventing the first flavour, vanilla flavour on the most popular dessert. Currently, the vanilla ice cream has been recorded as the world most impressive invention on The Guinness World Record. Even a three year old child knows what is vanilla ice cream.
==Ingredients in vanilla ice cream==
Basically, three main ingredients can found in a vanilla flavoured ice cream, that is Uranium oxide, U2O5, Hydrogen gas, H2 and Plastic (Polystyrene)
==Formula for creating a vanilla ice cream==
Yes, it is hard. Through you want to eat that ice cream, it is not an easy job. Just a vanilla ice cream, you have to follow many procedures to do it. Here are the formula:
===Vanilla cone===
A vanilla cone:
:<latex>{\pi} = 4\sum^\infty_{k=0} \frac{(-1)^k}{2k+1} = \frac{4}{1} - \frac{4}{3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \cdots\!</latex>
Two vanilla cone:
: <latex>\begin{align}
\pi &= \sqrt{12}\sum^\infty_{k=0} \frac{(-3)^{-k}}{2k+1}
= \sqrt{12}\sum^\infty_{k=0} \frac{(-1)^k}{3^k(2k+1)} \\
&= \sqrt{12}\left({1\over 3^0\cdot1}-{1\over 3^1\cdot3}+{1\over 3^2\cdot5}-{1\over 3^3\cdot7}+\cdots\right),
\end{align}</latex>
Where
: <latex>\pi_{0,1} = \frac{4}{1},\ \pi_{0,2} =\frac{4}{1}-\frac{4}{3},\ \pi_{0,3} =\frac{4}{1}-\frac{4}{3}+\frac{4}{5},\ \pi_{0,4} =\frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}, \ldots\! </latex>
In 1944, scientist anonymous has find out making a vanilla ice cream without using a cone. It is just like a crap melting in hand without using a cone to fill the ice cream in it. he produce a new formula:
:<latex>\frac2\pi = \frac{\sqrt2}2 \cdot \frac{\sqrt{2+\sqrt2}}2 \cdot \frac{\sqrt{2+\sqrt{2+\sqrt2}}}2 \cdot \cdots\!</latex>
:<latex>\frac{\pi}{2} = \prod^\infty_{k=1} \frac{(2k)^2}{(2k)^2-1} = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots\ = \frac{4}{3} \cdot \frac{16}{15} \cdot \frac{36}{35} \cdot \frac{64}{63} \cdots\!</latex>
Or:
:<latex>
\begin{align}
\pi &= 6 \arcsin \frac {1} {2} = 3 \sum_{n=0}^\infty \frac {\binom {2n} n} {16^n(2n+1)} \\
& = 6 \left( \frac {1} {2^1 \cdot 1} + \left( \frac {1} {2} \right) \frac {1} {2^3 \cdot 3} + \left( \frac {1 \cdot 3} {2 \cdot 4} \right) \frac {1} {2^5 \cdot 5} + \left( \frac{1 \cdot 3 \cdot 5} {2 \cdot 4 \cdot 6 } \right) \frac{1} {2^7 \cdot 7} + \cdots \right) \\
& = 3 + \frac{1}{8} + \frac{9}{640} + \frac{15}{7168} + \frac{35}{98304} + \frac{189}{2883584} + \frac{693}{54525952} + \frac{429}{167772160} + \cdots
\end{align}
</latex>
:<latex> \mu = \frac {(2n-1)^2} {8n(2n+1)}; \frac {1} {\mu} = \frac {8n(2n+1)} {(2n-1)^2} </latex>.
:<latex>\frac{\pi}{4} = 4 \, \arctan \frac{1}{5} - \arctan \frac{1}{239}\!</latex>
Which produces
:<latex>\arctan \, x = \sum^\infty_{k=0} \frac{(-1)^k x^{2k+1}}{2k+1} = x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7} + \cdots\!</latex>
and give
:<latex> \zeta(2)=\sum^\infty_{k=1} \frac{1}{k^2} = \frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \cdots\!</latex>
===Vanilla flavour in the ice cream===
Based on the theory of relativity, we can see the vanilla flavour in ice cream is counted on this possibility:
:<latex>
\pi=[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,2,1,84,\cdots]
</latex>
Or else:
:<latex>
\pi=3+\textstyle \cfrac{1}{7+\textstyle \cfrac{1}{15+\textstyle \cfrac{1}{1+\textstyle \cfrac{1}{292+\textstyle \cfrac{1}{1+\textstyle \cfrac{1}{1+\textstyle \cfrac{1}{1+\ddots}}}}}}}
</latex>
Or if you prefer this:
:<latex>
\pi=\textstyle \cfrac{4}{1+\textstyle \cfrac{1^2}{2+\textstyle \cfrac{3^2}{2+\textstyle \cfrac{5^2}{2+\textstyle \cfrac{7^2}{2+\textstyle \cfrac{9^2}{2+\ddots}}}}}}
=3+\textstyle \cfrac{1^2}{6+\textstyle \cfrac{3^2}{6+\textstyle \cfrac{5^2}{6+\textstyle \cfrac{7^2}{6+\textstyle \cfrac{9^2}{6+\ddots}}}}}
=\textstyle \cfrac{4}{1+\textstyle \cfrac{1^2}{3+\textstyle \cfrac{2^2}{5+\textstyle \cfrac{3^2}{7+\textstyle \cfrac{4^2}{9+\ddots}}}}}
</latex>
:<latex>
\pi = 16 \tan^{-1} \cfrac{1}{5} - 4 \tan^{-1} \cfrac{1}{239} 
= \cfrac{16} {5+\cfrac{1^2} {15+\cfrac{2^2} {25+\cfrac{3^2} {35+\ddots}}}} 
- \cfrac{4} {239+\cfrac{1^2} {717+\cfrac{2^2} {1195+\cfrac{3^2} {1673+\ddots}}}}.
</latex>
===Physical properties of vanilla ice cream===
In late 1961, many scientists found out that vanilla ice cream flavour can conduct electricity and produce heat which the particles of vanilla ice cream will have a higher kinetic energy. They do a research and measure their physical properties based on volume and density. They conclude it in a table as follows:
<latex>\pi=\frac{1}{Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{((2n)!)^3(42n+5)} {(n!)^6{16}^\!</latex>
<latex>\pi=\frac{4}{Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(-1)^n(4n)!(21460n+1123)} {(n!)^4{441}^{2n+1}{2}^</latex>
<latex>\pi=\frac{4}{Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(6n+1)\left ( \frac{1}{2} \right )^3_n} (n!)^3}\!</latex>
<latex>\pi=\frac{32}{Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \left (\frac{\sqrt{5}-1}{2} \right )^{8n} \frac{(42n\sqrt{5} +30n + 5\sqrt{5}-1) \left ( \frac{1}{2} \right )^3_n} (n!)^3}\!</latex>
<latex>\pi=\frac{27}{4Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \left (\frac{2}{27} \right )^n \frac{(15n+2)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{3} \right )_n \left ( \frac{2}{3} \right )_n} {(n!)^3}\!</latex>
<latex>\pi=\frac{15\sqrt{3}}{2Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \left ( \frac{4}{125} \right )^n \frac{(33n+4)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{3} \right )_n \left ( \frac{2}{3} \right )_n} {(n!)^3}\!</latex>
<latex>\pi=\frac{85\sqrt{18\sqrt{3}Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \left ( \frac{4}{85} \right )^n \frac{(133n+8)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{6} \right )_n \left ( \frac{5}{6} \right )_n} {(n!)^3}\!</latex>
<latex>\pi=\frac{5\sqrt{5}}{2\sqrt{3}Z} \!</latex>	<latex>Z=\sum_{n=0}^{\infty } \left ( \frac{4}{125} \right )^n \frac{(11n+1)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{6} \right )_n \left ( \frac{5}{6} \right )_n} {(n!)^3}\!</latex>
<latex>\pi=\frac{2\sqrt{3}}{Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(8n+1)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} {(n!)^3{9}^{n}}\!</latex>
<latex>\pi=\frac{\sqrt{3}}{9Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(40n+3)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} {(n!)^3{49}^\!</latex>
<latex>\pi=\frac{2\sqrt{11Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(280n+19)\left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} {(n!)^3{99}^\!</latex>
<latex>\pi=\frac{\sqrt{2}}{4Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(10n+1) \left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} {(n!)^3{9}^\!</latex>
<latex>\pi=\frac{4\sqrt{5}}{5Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(644n+41) \left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} {(n!)^35^n{72}^\!</latex>
<latex>\pi=\frac{4\sqrt{3}}{3Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(-1)^n(28n+3) \left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} { (n!)^3{3^n}{4}^\!</latex>
<latex> \pi=\frac{4}{Z}\!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(-1)^n(20n+3) \left ( \frac{1}{2} \right )_n \left ( \frac{1}{4} \right )_n \left ( \frac{3}{4} \right )_n} { (n!)^3{2}^\!</latex>
<latex>\pi=\frac{72}{Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(-1)^n(4n)!(260n+23)}{(n!)^44^{4n}18^\!</latex>
<latex>\pi=\frac{3528}{Z} \!</latex> 	<latex>Z=\sum_{n=0}^{\infty } \frac{(-1)^n(4n)!(21460n+1123)}{(n!)^44^{4n}882^\!</latex>
==Facts for consuming vanilla ice cream==
After you eating this vanilla ice cream, you may become like this:
Or Like This:
==Precaution==
Danger! Please follow the instructions before using this item. This item is highly flammable and explosive. So don't eat it. After produce it, discard it. Or, it can be used in a terrorist attack. Thus, think before you get know and make this crap. It is same with others crap. Thanks.
Vanilla Ice Cream is dangerous!!! Run as fast as you can if you see it!!! RUN!!!
==See also==
*Vanilla
*Ice cream
*Antimatter
*Whatever
Category:Desserts
Category:Things that go Boom