Thursday, November 9, 2017

calculus - Evaluating the series $sumlimits_{n=0}^{infty}frac{n}{3^n}$




Hello all, I have one last major question, where would I get started on the following question:


$$\sum_{n=0}^{\infty}\frac{n}{3^n}$$


I know it is a series (obviously), and I think it is geometric, but I have no idea as to how to start it. Does anyone have any first steps/tips as to what I could do for this?


Thanks so much in advance!


Edit: Per the first comment on my posting, by 1hf, see:


Very close to How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$



In particular, see the answer at How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$


Thanks all!

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