CPM Homework Help : PC3 Problem 13-157

Use the definition of $e$ as a limit to determine the exact values of the following limits.

Hint:

$e= \lim \limits_{n\to\infty}\left(1+\frac{1}{n}\right)^{n}$

$\lim \limits _ { n \rightarrow \infty } ( 1 + \frac { 5 } { n } ) ^ { n }$
Step (a):
Let $n = 5k$ .
$\lim \limits_{5k\to\infty}\left(1+\frac{5}{5k}\right)^{5k}$

$\lim \limits _ { n \rightarrow \infty } ( 1 + \frac { 1 } { 2 n } ) ^ { n }$
Hint (b):
Let $n = k/2$ .