Prove $\sum\limits_{n\ge0}\frac{(-1)^n}{(2n+1)^3}=\frac{\pi^3}{32}$
49936
Various evaluations of the series $\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)^3}$
101017
What is the sum of $\sum\limits_{i=1}^{n}ip^i$?
35529
Prove that $\sin x+2x\ge\frac{3x(x+1)}{\pi}$ for all $x\in [0,\frac{\pi}{2}]$
130543
If $a_n = \sum\limits_{r=0}^n \binom{n}{r} b_r$, prove $(-1)^n b_n = \sum\limits_{s=0}^n \binom{n}{s} (-1)^s a_s$
35027
Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+...+a_n)^2 $
153231
Why does $\sum_1^\infty \frac1{n^3}=\frac52\sum_1^\infty\frac{(-1)^{n-1}}{n^3\binom{2n}{n}}$?
60197
Infinite Series $\sum\limits_{n=1}^\infty\frac{x^{3n}}{(3n-1)!}$
23557
Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$
135032
Nature of the series $\sum\limits_{n=3}^{\infty} \frac{1}{(\log\log n)^{\log n}}$
78712
Prove that $\frac{1}{\sin^2 z } = \sum\limits_{n= -\infty} ^ {+\infty} \frac{1}{(z-\pi n)^2} $
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
89698
Please help with $\sum\limits_{r=1}^{N}\frac{2r+3}{3^r(r+1)}$
22636
Find the sum of the series $\sum \limits_{n=1}^{\infty} \frac{2^{-n}(n+3)}{(n+1)(n+2)}$
32866
How find this sum $\sum\limits_{n=0}^{\infty}\frac{1}{(3n+1)(3n+2)(3n+3)}$
91784
Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
22524
Proving that $\frac{\pi^{3}}{32}=1-\sum_{k=1}^{\infty}\frac{2k(2k+1)\zeta(2k+2)}{4^{2k+2}}$
132126
Proving $\sum\limits_{n=1}^{\infty } \frac{\mu (n)}n=0$ where $\mu$ is the Möbius function