Computing $\sum_{n=1}^ \infty n^2 \cdot \left(\frac{2}{3}\right)^n$
7686
How to prove $\sum_{n=0}^{\infty} \frac{n^2}{2^n} = 6$?
98933
Calculating the sum of $f(x) = \sum_{n=0}^{\infty} {n \cdot 2^n \cdot x^n}$
45440
$\sum_{n=2}^\infty \frac{1}{(\ln\, n)^2}$ c0nvergence
7177
Find sum of series $ \sum_{n=1}^{\infty} (n\cdot \ln \frac{2n+1}{2n-1} - 1) $
157972
Find a closed form expression for $\sum\limits_{i=0}^{\infty} i^2\cdot x^i$
124002
How prove this series $\sum_{n=1}^{\infty}\frac{e^n\cdot n!}{n^n}$ divergent
25395
Sum $\sum_{n=1}^\infty \frac{n^2}{(n+2)!}$
89771
$\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right]$
109901
Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
108010
Evaluating $\sum_{k=1}^{\infty}\left(\frac{\sin(tk)}{k}\right)^2$
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
133955
Compute: $\sum_{k=1}^{\infty}\sum_{n=1}^{\infty} \frac{1}{k^2n+2nk+n^2k}$
26370
Consider convergence of series: $\sum_{n=1}^{\infty}\sin\left[\pi\left(2+\sqrt{3}\right)^n\right]$
162
Determine the convergence of $ \sum_{n=1}^{\infty}\left[1-\cos\left(1 \over n\right)\right] $
155873
Evaluate $\lim\limits_{n\rightarrow \infty}\frac{n+n^2+n^3+\cdots +n^n}{1^n+2^n+3^n+\cdots +n^n}.$
126304
Determining bounds for the sum $\sum\limits_{n=1}^\infty \frac{1}{2^n - 3^n }$
99003
How do we calculate this sum $\sum_{n=1}^{\infty} \frac{1}{n(n+1)\cdots(n+p)}$?