Chapter 6.2, Problem 109E

In the following exercises, using a substitution if indicated, express each series in terms of elementary functions and find the radius of convergence of the sum.

109. Differentiate the series $Ex={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{x^n}{n!}}$ term-by-term to show that E(x) is equal to its derivative.