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

I have no idea to calculate this sum. I　try shift index since $k=0$ gives 0, tis won't change the sum. But I don't know how to keep going. Can someone give me a hint or suggestion to calculate this sum? Thanks

Hint. Probably you know that $x\not=1$,
$$\sum_{k=0}^{N-1}x^k=\frac{1-x^{N}}{1-x}.$$
What happens if you differentiate both sides?
