Chapter 6.1, Problem 39E

In the following exercises, given that $\begin{array}{l}\frac{1}{1-x}\text{=}{\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{x}^n}\\ \end{array}$ with convergence in (− 1, 1), find the power series for each function with the given center a, and identify its interval of convergence.

39. $f(x)=\frac{1}{1-2x};a=0.$