Chapter 9.9, Problem 21E

Using a Power Series In Exercises 19-28, use the power series

$\frac{1}{1+x}={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{(-1)}^n{x}^n,\left|x\right|<1}$ to find a power series for the function, centered at 0, and determine the interval or convergence.

$f(x)=\ln (x+1)={\displaystyle \int \frac{1}{x+1}dx}$