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Neves
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I'm a software developer interested in the recreational side of mathematics.

$$ \displaystyle(x+y)^{z}=x^z+\frac{z}{1!} x^{z-1}y^1+\frac{z(z-1)}{2!} x^{z-2}y^2+\frac{z(z-1)(z-2)}{3!} x^{z-3}y^3+\cdots $$

«O Binómio de Newton é tão belo como a Vénus de Milo.
O que há é pouca gente para dar por isso.
óóóó---óóóóóó óóó---óóóóóóóóóóóóóóó
(O vento lá fora.)»

Álvaro de Campos.

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80
How to prove this identity $\pi=\sum\limits_{k=-\infty}^{\infty}\left(\frac{\sin(k)}{k}\right)^{2}\;$?
Mar 15, 2013
61
Funny identities
Nov 11, 2010
45
Prime powers, patterns similar to $\lbrace 0,1,0,2,0,1,0,3\ldots \rbrace$ and formulas for $\sigma_k(n)$
Dec 29, 2010
26
Riemann's zeta as a continued fraction over prime numbers.
Apr 8, 2014
26
Proving that $\frac{\pi}{4}$$=1-\frac{\eta(1)}{2}+\frac{\eta(2)}{4}-\frac{\eta(3)}{8}+\cdots$
Sep 3, 2013
24
Finding the value of $\sum\limits_{k=0}^{\infty}\frac{2^{k}}{2^{2^{k}}+1}$
Apr 8, 2013
20
Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
Dec 19, 2013
20
Arithmetic of continued fractions, does it exist?
Oct 26, 2011
19
Proving that $\left(\frac{\pi}{2}\right)^{2}=1+\sum_{k=1}^{\infty}\frac{(2k-1)\zeta(2k)}{2^{2k-1}}$.
Dec 18, 2013
17
How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$
Jan 17, 2012
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The Riemann's Zeta Function represented as a continued fraction and a question of convergence
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