Chapter 9.9, Problem 30E

Approximating a Sum In Exercises 31 and 32, (a) use a graphing utility to graph several partial sums of the series. b) find the sum of the series and its radius of convergence,(c) use a graphing utility and 50 terms of the series to approximate the sum when $x=0.5$ . and (d) determine what the approximation represents and how good the approximation is.

${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{{(-1)}^n{x}^{2n+1}}{(2n+1)!}}$