Sum $S=\sum _{k=1}^{\infty } \frac{(-1)^k H_k}{k^3}?$
66380
Alternating harmonic sum $\sum_{k\geq 1}\frac{(-1)^k}{k^3}H_k$
139430
How to prove that $\sum_{n=1}^{+\infty}\frac{1}{n^2+1}=\frac{-1+\pi \coth (\pi)}{2}$?
138542
Evaluating sums question $\sum_{k=2}^n \frac{1}{k^2-1}$
127806
How to find the sum of the series $\sum_{k=2}^\infty \frac{1}{k^2-1}$?
57372
Series convergence of $\sum_{n=1}^{\infty}\frac{1}{n^3}$
152802
How find series $\sum_{n=1}^{\infty}\frac{(-1)^{[\sqrt[m]{n}]}}{n^a}$?
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
60104
Evaluate $\sum_{k=1}^\infty\frac{x^k}{k(k+1)}$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
114280
Computing $\sum_{n=1}^∞\frac{1}{(n+1)(n+2)(n+3)....(n+p)}$
111602
Help with telescoping sum $\sum_{i=3}^n \frac{1}{i(i+3)} $
142985
Finding sum of series $\sum^{\infty}_{k=0}\frac{(k+1)(k+2)}{2^k}$
6436
Proving an alternating Euler sum: $\sum_{k=1}^{\infty} \frac{(-1)^{k+1} H_k}{k} = \frac{1}{2} \zeta(2) - \frac{1}{2} \log^2 2$
133955
Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
74117
Find the sum of series $\sum_{n=0}^{\infty}\frac{z^{kn}}{(kn)!}$
134610
Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$