Chapter 9, Problem 82RE

Finding Intervals of Convergence In Exercises 89 and 90, find the intervals of convergence of (a) f(x). (b) $f^{\text{'}}(x)$ (c) $f^{\text{'}}(x)$ and (d) ${\displaystyle \int f(x)dx}$ . (Be sure to include a check for convergence at the endpoints of the intervals.)

$f(x)={\displaystyle \underset{n=1}{\overset{\infty }{\sum }}\frac{{(-1)}^{n+1}{(x-4)}^n}{n}}$