Chapter 6.3, Problem 163E

[T] In the following exercises, identify the value of x such that the given series ${\displaystyle \underset{n=0}{\overset{\infty }{\sum }}{a}_n}$ is the value of the Maclaurin series of f(x) at x. Approximate the value of f(x) using $S_{10}={\displaystyle \underset{n=0}{\overset{10}{\sum }}{a}_n}$ .

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