$3(1-3x)^{-2}=\sum_{n=0}^{\infty}(n+1)3^nx^n.$ How?
6416
How can I evaluate $\sum_{n=0}^\infty(n+1)x^n$?
92810
What is $\sum_{r=1}^\infty\frac{r+2}{2^{r+1}(r)(r+1)}$?
52987
$\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
111705
Why does $\frac{1+t}{(1-t)^3}=\sum_{n=0}^{\infty}(1+n)^2t^n$
4253
How to calculate: $\sum_{n=1}^{\infty} n a^n$
126385
How to prove $a^3 + b^3 +c^3 - 3abc =1 $, If a,b,c are infinite series as given in the description box below?
80177
Sum from $n=1$ to $N$ of $\sin(nx)/2^n$
78542
What is $\sum_{n=1}^{\infty} \frac{n}{2^{\sqrt{n}}}$?
69498
What is $\sum_{r=0}^n \frac{(-1)^r}{\binom{n}{r}}$?
47706
Find the value of $ \sum_{n=1}^{\infty} \frac{n^3}{3^n} $
14883
Find $\sum_{n=1}^{\infty}$ $\frac{n^{2}}{\left(n+1\right)\left(n+2\right)\left(n+3\right)\left(n+4\right)}$
2877
Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
37650
Find $\sum_{m=0}^n\ (-1)^m m^n {n \choose m}$
43320
Find the sum of the power series $\sum_{n=1}^\infty n*(n+1)*x^n$
55339
Find the sum $\sum_{n=1}^{\infty}\frac{ 1}{n^{2}(2n-1)}$
118456
Find $\sum_{n=1}^{\infty}\tan^{-1}\frac{2}{n^2}$
134311
How to determine equation for $\sum_{k=1}^n k^3$