Expected value of probability distribution

The number $\displaystyle X$ of particles emitted as the result of an experiment is a random variable with probability distribution:

$\displaystyle P(X=k)=\left(\frac{1}{2}\right)^{k+1}\ for\ k \geq 0$

What is the expected number of particles emitted during one experiment

This is how I've gone so far:

$\displaystyle E(X)=\sum_{k=0}^{\infty}kP(X=k)$

$\displaystyle =\left(\frac{1}{2}\right)^2+2\left(\frac{1}{2}\rig ht)^3+ 3\left(\frac{1}{2}\right)^4+...$

I'm confused as to how to evaluate this sum