Chapter 9.10, Problem 4ES

(a) Use the Maclaurin series for $1/(1-x)$ to find the Maclaurin series for $1/(a-x),$ where $a\ne 0,$ and state the radius of convergence of the series.

(b) Use the binomial series for $1/{(1+x)}^2$ obtained in Example 4 of Section 9.9 to find the first four nonzero terms in the Maclaurin series for $1/{(a+x)}^2,$ where $a\ne 0,$ and state the radius of convergence of this series.