CPM Homework Help : PCT Problem 8-71

Find the following sums. You can use your SUM program or the sum sequence commands from your calculator.

$\displaystyle \sum _ { k = 0 } ^ { 4 } \frac { 1 } { k ! }$
Answer (a):
$=\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+\frac{1}{3!}+\frac{1}{4!} =1+1+\frac{1}{2}+\frac{1}{6}+\frac{1}{24} =2.708333$

$\displaystyle \sum _ { k = 0 } ^ { 10 } \frac { 1 } { k ! }$
Answer (b):
$2.71828$

What is the value of $\lim\limits _ { n \rightarrow \infty } \sum _ { k = 0 } ^ { n } \frac { 1 } { k ! }$ ?
Answer (c):
$e$