Chapter 11 - Infinite Sequences and Series - 11.10 Exercises - Page 789: 19

$cosx=\Sigma_{n=0}^{\infty}(-1)^{n+1}\frac{(x-\pi)^{2n}}{(2n)!}$ The radius of convergence is $R=\infty$.

Taylor series centered at $a= \pi$ is $-1+\frac{1}{2!}(x-\pi)^{2}-\frac{1}{4!}(x-\pi)^{4}+....$ $cosx=\Sigma_{n=0}^{\infty}(-1)^{n+1}\frac{(x-\pi)^{2n}}{(2n)!}$ The radius of convergence is $R=\infty$.