sequences and series - How do you prove $sum frac {n}{2^n} = 2$?

How do you prove

$$\sum_{n=1}^{\infty} \frac {n}{2^n} = 2\ ?$$

My attempt: I have been trying to find geometric series that converge to 2 which can bind the given series on either side. But I am unable to find these. Is there a general technique to find the sum? This is a high school interview question and must be easy enough to solve in a few minutes.

Please give any hints for the first step towards a solution.

Answer

Hint: Denote your sum by $S$, rewrite $S=2S-S$ and try to rewrite the sums.