Chapter 11 - Infinite Sequences and Series - 11.10 Exercises - Page 789: 32

$\Sigma_{n=0}^{\infty}\dfrac{(1+2(-1)^{n})x^{n}}{n!}$ $R=\infty$

$e^{x}+2e^{-x}=\Sigma_{n=0}^{\infty}\frac{x^{n}}{n!}+2\Sigma_{n=0}^{\infty}\dfrac{(-x)^{n}}{(n)!}$ $=\Sigma_{n=0}^{\infty}\dfrac{(1+2(-1)^{n})x^{n}}{n!}$ $R=\infty$