Hello

I was wondering if there was any way to calculate the sum of the series

$\displaystyle \sum_{k=1}^\infty \frac{k}{2^k}$

I know it is convergent by the ratio test, but it there anyway to finding out what sum it converges to?

This series came up when I was calculating the expected value of a random variable.

(Wolfram Alpha says it is 2, which makes sense in context of the problem)