Prove that $\prod_{k=2}^{+\infty} (1+1/k^2) = \sinh(\pi)/(2 \pi)$.
13796
What is the value of $\prod_{n=1}^\infty (1+\frac{1}{n^2})$?
84595
How to evaluate $\lim\limits_{n\to+\infty} \prod\limits_{k=1}^n (1+k/n^2)$?
122169
Prove $\sin(\pi/2)=1$ using Taylor series
141404
Infinite product: $\prod_{k=2}^{n}\frac{k^3-1}{k^3+1}$
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
17241
How to prove $ \prod_{d|n} d= n^{\frac{\tau (n)}{2}}$
23919
Trying to evaluate $\prod_{k=1}^{n-1}(1-e^{2k\pi i/n})$ for my complex analysis homework
15259
Proving $\prod \limits_{k=0}^{n}(1-a_k) \geq1- \sum\limits_{k=0}^{n}a_k$
132182
$\sum_{n=1}^\infty \sum_{m=1}^\infty\frac{1}{(m+n)^2}$
156367
How to prove that $\sum\limits_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)...(n+k)} = \frac{1}{kk!}$ for every $k\geqslant1$
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
22524
Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
28254
Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
84949
Evaluate $\prod_{n=1}^\infty \frac{2^n-1}{2^n}$
21941
Proving: $x = a_0 + \sum_{n=1}^{\infty}(a_n \cos nx + b_n \sin nx)$
37484
Is there an elementary argument to show that $\prod_{n=0}^\infty \frac{2n+1}{2n+3}=0$