Prove $\sum_{n=1}^{\infty}\sum_{m=1}^{\infty}\frac{m^2-n^2}{(m^2+n^2)^2}=\frac{\pi}{4}$
54604
Evaluate $ \sum_{m > n > 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} $
125915
An Infinite Double Summation $\sum_{k=1}^{\infty} \sum_{n=1}^{\infty} \frac{1}{n^2k^2(n+k)^2}$?
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
71240
The limit of a sum $\sum_{k=1}^n \frac{n}{n^2+k^2}$ as $n\rightarrow\infty$
44970
Show $\sum_{n=0}^\infty\frac{1}{a^2+n^2}=\frac{1+a\pi\coth a\pi}{2a^2}$
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
25967
Prove $\csc(x)=\sum_{k=-\infty}^{\infty}\frac{(-1)^k}{x+k\pi}$
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
155005
How to show $\sum_{k=n}^\infty{\frac{1}{k!}} \leq \frac{2}{n!}$
55339
Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$
28378
Find the infinite sum of the series $\sum_{n=1}^\infty \frac{1}{n^2 +1}$
115912
Summation inductional proof: $\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+\ldots+\frac{1}{n^2}<2$
7686
How to prove $\sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6$?
153226
Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
132126
Proving $\sum\limits_{n=1}^{\infty } \frac{\mu (n)}n=0$ where $\mu$ is the Möbius function
30407
Prove that $\sum_{n=1}^\infty\frac{n}{n^2+1}$ is divergent