Evaluate $\sum_{n=1}^{\infty}\arctan (\frac{2}{n^2})$
36023
Showing that $ \sum_{n=1}^{\infty} \arctan \left( \frac{2}{n^2} \right) =\frac{3\pi}{4}$
118456
Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$
76050
Test for convergence of the series $\sum_{n=1}^{\infty}\frac{n}{\sqrt{n^2 +1}}$
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
14223
Find the infinite sum $\sum_{n=1}^{\infty}\frac{1}{2^n-1}$
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
17686
Evaluate the infinite series $\sum_{r=1}^{\infty} \frac{2^{-r}}{r^{2}}$
66568
Number Theory : Show that $\sum_{i=0}^\infty$ $ [\frac{n}{2^i}+\frac{1}{2}]$ $=$ $2n$
141390
Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
91784
Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
63863
Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$
152698
Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$
153989
How to evaluate the sum $\frac{1}{\sqrt{n}}+\frac{1}{\sqrt{2n}}+\cdots+\frac{1}{\sqrt{n^2}}$ when $n$ grows?
24022
Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
150563
Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$
74120
Find the value of $\sum_{n=1}^{\infty} \frac{2}{n}-\frac{4}{2n+1}$
25503
Convergence of $\sum_{n=1}^\infty \frac{\sin^2(n)}{n}$