Hi, all. I need to evaluate the following:

$\displaystyle \frac{1}{k}\sum_{n = 0}^{\infty}(\frac{k-1}{k})^nn$

wherek∈ℕ andk≠1

I don't really know how to do much else than test whether or not a series converges or diverges; I don't know how to determine what it convergesto.

Thanks, guys!