If $|z| < 1 $ , calculate $ s= \sum_{n=1}^{\infty} n^2 \cdot z^n $
61547
Derive an explicit formula for a power series $\sum_{n=1}^\infty n^2x^n$
140614
Show that $\sum^\infty_{n=m}\frac{1}{n^2} = O(\frac{1}{m})$
57780
$\sum_{i=1}^n i\cdot i! = (n+1)!-1$ By Induction
154544
Prove that $ \sum_{n=0}^\infty \frac{z^{2^n}}{1-z^{2^{n+1}}}=\frac{z}{1-z} $
91933
Evaluate $\sum_{k=1}^nk\cdot k!$
7727
Convergence of series $\sum_{n=1}^\infty\sin(n)\cdot\sin(1/n)$
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
156720
Evaluate $\sum_ {n=1}^{\infty} \cot^{-1}(2n^2)$
98941
Closed formula for the sums $\sum\limits_{1 \le i_1 < i_2 < \dots < i_k \le n} i_1 i_2 \cdots i_k $?
115420
Evaluate $\sum_{n=1}^{\infty} \frac{n}{n^4+n^2+1}$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
101052
Find the infinite sum $\sum_{k=1}^{\infty}\sqrt k - 2\sqrt {k + 1} + \sqrt {k + 2} $
145798
Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$
56961
Evaluate the limit of $\sum_{n=1}^{\infty}\frac{n^2}{n!}$
107976
Find a closed formula for $\sum_{n=1}^\infty nx^{n-1}$
138313
How to sum $\sum_{n=1}^{\infty} \frac{1}{n^2 + a^2}$?
7177
Find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $