Chapter 9.4, Problem 51E

Evaluating an infinite series Let f(x) = (e^x − 1)/x, for x ≠ 0, and f(0) = 1. Use the Taylor series for f about 0 and evaluate f(1) to find the value of ${\displaystyle \underset{k=0}{\overset{\infty }{\sum }}\frac{1}{(k+1)!}}$.