An arithmetic-geometric series

Evaluate $\displaystyle\sum_{n=1}^\infty \dfrac{n^2}{2^n}$ .

Show hints (2)+

Start from $\sum x^n=1/(1-x)$ ; differentiate and multiply by $x$ to bring down a factor of $n$ .
Do it twice for $n^2$ , then set $x=1/2$ .

Answer

Reveal answer →

Create a free account to see the full worked solution and track your progress.