Chapter 9.2, Problem 31E

Combining power series Use the geometric series

$f(x)=\frac{1}{1-x}={\displaystyle \underset{k=0}{\overset{\infty }{\sum }}{x}^k},\text{for}\left|x\right|<1,$

to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series.

31. $h(x)=\frac{2x^3}{1-x}$