Chapter 9, Problem 45RE

Convergence Write the remainder term R_n(x) for the Taylor series for the following functions centered at the given point a. Then show that $\underset{n\to \infty }{\lim }|R_n(x)|=0$, for all x in the given interval.

45. $f(x)=ln(1+x),a=0,-\frac{1}{2}\le x\le \frac{1}{2}$