Proving $ \sum_{n=1}^{\infty} nz^{n} = \frac{z}{(1-z)^2}$ for $z \in (-1, 1)$
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
125701
Prove that $-2\log(2) = -2 + \sum_{n=1}^{\infty}\frac{1}{n(2n+1)}$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
725
proof of $\sum_{n=1}^\infty n \cdot x^n= \frac{x}{(x-1)^2}$
125933
On the series $\sum \limits_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
104646
Question on simplification of $\sum_{n=1}^{\infty}\frac{2}{(2n+1)(2n+3)}$?
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
150563
Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
91784
Calculating $\sum_{n=1}^\infty {\frac{1}{2^nn(3n-1)}}$
93690
How to obtain the sum of the following series? $\sum_{n=1}^\infty{\frac{n^2}{2^n}}$
59253
Summing the power series $\sum\limits_{n=0}^\infty (-1)^n \frac{x^{2n+1}}{2n+1}\prod\limits_{k=1}^n\frac{2k-1}{2k} $
44928
Show $\sum_n \frac{z^{2^n}}{1-z^{2^{n+1}}} = \frac{z}{1-z}$
140614
Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
12480
Convergence of $\sum_{n=1}^{\infty} \frac{\frac{1}{2}+(-1)^n}{n}$