Find the sum of this series May I know how I should go about finding the sum of this series? 
$\displaystyle\sum_{n=1}^\infty$ $\dfrac{n}{2^{n-1}}$
I am really stuck. Thanks!

$$s=\sum_{n=1}^\infty \dfrac{n}{2^{n-1}}=1+2/2+3/2^2+4/2^3+5/2^4+....(1)$$
By dividing whole equation by $2,$
$$\dfrac{s}{2}=\dfrac{1}{2}(\sum_{n=1}^\infty \dfrac{n}{2^{n}})=1/2+2/2^2+3/2^3+4/2^4+5/2^5+....(2)$$
Now$(1)-(2)$ gives us,
$$\dfrac{s}{2}=1+1/2+1/2^2+1/2^3+1/2^4+....=1+1$$
Hence we can obtain $s=4.$
