How I can calculate $\sum_{n=0}^\infty{\frac{n}{3^n}}$? For more than one series of any search function known not seem to find the sum of this series:
$$\sum_{n=0}^\infty{\frac{n}{3^n}}$$
I've found that converges with the quotient criterion.
Could you give me some suggestions for finding the sum of this series?
Thanks!

HINT:
If $|a|<1$,$$a\sum_{0\le n<\infty}r^n=\frac a{1-r}$$ (Proof)
Differentiate wrt $r$
