Sum of the series $sum frac{n}{2^{n}}$

I know that the series converges by d'Alembert ratio test, where $\lim\left ( \frac{A_{n+1}}{A_{n}} \right )= \frac{1}{2}$, but I don't know how to calculate the sum of the serie. Thanks for the help.

Answer

$\sum_{k=0}^\infty x^n = \frac{1}{1-x}$ for $|x|<1$.
Then
$\sum_{k=1}^\infty nx^n = x\times \left(\frac{1}{1-x}\right)'$ for $|x|<1$.