Chapter 6.2, Problem 92E

In the following exercises, evaluate each infinite series by identifying it as the value of a derivative or integral of geometric series.

92. Evaluate ${\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{n}{3^n}}$ as $f\text{'}\left(\frac{1}{3}\right)$ where. $f(x)={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{x}^n.}$