Chapter 9.9, Problem 39E

Using a Power Series In Exercises 37-40, use the power series

$\frac{1}{1-x}={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{x}^n,}\left|x\right|<1$

to find a power aeries for the function, centered at 0, and determine the interval of convergence.

$f(x)=\frac{1+x}{{(1-x)}^2}$