$$\sum _{n=0}^{\infty }\left(\frac{n+1}{2^n}\right)$$
I know that I can separate it into: $\sum _{n=0}^{\infty }\left(\frac{n}{2^n}+\frac{1}{2^n}\right)$
And I am able to prove that the second part gives the sum 2, but the first one is a bit problematic, any tips?
