Chapter 9, Problem 25RE

Power series from the geometric series Use the geometric series ${\displaystyle \underset{k=0}{\overset{\infty }{\sum }}{x}^k=\frac{1}{1-x}}$, for |x| < 1, to determine the Maclaurin series and the interval of convergence for the following functions.

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