Chapter 11 - Section 11.8 - Power Series - 11.8 Exercises - Page 786: 13

$R=\infty$ ; interval of convergence is $(-\infty, \infty)$

Let $a_{n}=\frac {x^{n}}{n!}$, then $\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac {x^{n+1}}{(n)!}}{\frac {x^{n}}{n!}}|$ $=0\lt 1$ Hence, $R=\infty$ ; interval of convergence is $(-\infty, \infty)$