Chapter 9.2, Problem 32E

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.

32. $f{(x)}^3=\frac{1}{1-x^3}$