# Sum of the series $\sum_{1}^{\infty}\frac{n}{2^{n}}.$ [duplicate]

Sum of the series $\sum_{1}^{\infty}\frac{n}{2^{n}}$ is

$a.1$

$b.2$

$c.3$

$d.4$

Hint: $${\frac {x}{(1-x)^{2}}}=\sum _{n=1}^{\infty }nx^{n}\quad {\text{ for }}|x|<1\!$$ let $x=\frac{1}{2}$ to get what you want