I'm struggling with finding this sum:


Any pointers would be greatly appreciated.

I have not found any information of use elsewhere, but maybe I am using the wrong search terms.


Let $S=\sum\limits_{i=0}^{\infty}\frac{i}{4^i}$, so $4S=\sum\limits_{i=1}^{\infty}\frac{i}{4^{i-1}}=\sum\limits_{i=0}^{\infty}\frac{i+1}{4^i}$, so:




Not the answer you're looking for? Browse other questions tagged or ask your own question.