CPM Homework Help : PC3 Problem 13-64

Use a calculator to evaluate each of the following sums. Recall that $5!$ , for example, means $5 · 4 · 3 · 2 · 1$ .

$\displaystyle\sum _ { k = 0 } ^ { 4 } \frac { 1 } { k ! }$
Step (a):
$=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!}$

What is the value of $\lim \limits _ { n \rightarrow \infty } \displaystyle \sum _ { k = 0 } ^ { n } \frac { 1 } { k ! }$ ?