What is the closed form for $ \sum_{n=1}^{\infty}n\theta^n, 0 \lt \theta \lt 1$?
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
43903
Find the sum for $\sum_{n=1}^{\infty}(-1)^{(n+1)}\frac{2n+1}{3^n} $
116491
Closed form for $\sum_{k=0}^{m} {\binom {m}{k}} a^{k} (b+ck)^N$
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
67271
$\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$
63900
Convergent or divergent series: $\sum_{n=1}^{\infty} \sqrt{a_n \cdot a_{n+1}}$?
146762
Closed form for $\sum_{k=0}^{n} \binom{n}{k}\frac{(-1)^k}{(k+1)^2}$
136444
Evaluating $\sum_{n=0}^\infty\frac{(-1)^n}{3n+1}$
140462
Find a closed form for the power series $f_p(x)=\sum\limits_{n=0}^\infty\frac{n^p}{n!}x^n$
114031
Show that $\sum_{n=0}^\infty r^n e^{i n \theta} = \frac{1- r\cos(\theta)+i r \sin(\theta)}{1+r^2-2r\cos(\theta)}$
125933
On the series $\sum \limits_{n=2}^{\infty} \frac{(-1)^n}{n \log n}$
125813
Convergence of $ \sum_{n=1}^\infty\left(\exp(\frac{(-1)^n}{n})-1\right)$?
49982
Closed expression for infinite series
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
141390
Closed form for $\sum_{n=-\infty}^\infty \frac{1}{(z+n)^2+a^2}$
145798
Generalizing $\sum \limits_{n=1}^{\infty }n^{2}/x^{n}$ to $\sum \limits_{n=1}^{\infty }n^{p}/x^{n}$
152698
Evaluation of $\sum_{n=0}^{\infty}\frac{1}{(n^4+n^2+1)n!}$