Is it possible to find the sum of the infinite series $1/p + 2/p^2 + 3/p^3 + \cdots + n/(p^n)+\cdots$, where $p>1$? Is it possible to find the sum of the series:
$$\frac{1}{p} + \frac{2}{p^2} +\frac{3}{p^3} +\dots+\frac{n}{p^n}\dots$$ 
Does this series converge? ($p$ is finite number greater than $1$)

Hint:
$$\frac{1}{1-x}=1+x+x^2+\dots$$
Differentiate this formula (it is uniformly convergent for $|x|<1$) and multiply with x. Finally set $x=1/p$.
