Integral form of $2\sum_{k=1}^{\infty}\frac{(2k-1)^2-1}{(2k-1)^4+(2k-1)^2+1}$
50606
Find $\sum\limits_{k\, \text{ odd}} \frac{2(k^2-1)}{k^4+k^2+1}$
28254
Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?
110996
Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
55339
Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$
124445
Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
52987
$\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
141390
Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
16776
How to prove $\sum_{m=1}^\infty \sum_{n=1}^\infty \frac{1}{m^2+n^2}=+\infty$
130548
What is the sum of the power series: $\sum_{k=2}^\infty\frac{x^k}{k(k-1)}$?
81589
Find the sum of $\sum_{k=0}^{\infty} 1/[(r+2k+2)(s+2k+2)]$
33986
Calculate $\sum_{n=1}^{\infty}(\frac{1}{2n}-\frac{1}{n+1}+\frac{1}{2n+4})$
17686
Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
17713
What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
115420
Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$