How do I find the summation of this series?

Question

$$\sum_{x=0}^{\infty}\frac{x}{2^{x}}$$

This looks like a geometric series but the $x$ is throwing me off. I don't know how to proceed. Any help would be greatly appreciated.

do you mean $$\sum_{n=0}^{\infty}\frac{n}{2^n}$$ – Dr. Sonnhard Graubner Jul 10 '17 at 18:20 — Dr. Sonnhard Graubner, Jul 10 '17 at 18:20

score 0 · Answer 1 · answered Jul 10 '17 at 18:21

0

You could show by induction that $$\sum_0^n \frac {x}{2^x} = 2^{-n}(-n+2^{n+1}-2)$$ and then use the limit on that.

answered Jul 10 '17 at 18:21

Börge

1 Answers1