### Home > PC3 > Chapter 13 > Lesson 13.3.5 > Problem13-157

13-157.

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

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

1. $\lim \limits _ { n \rightarrow \infty } ( 1 + \frac { 5 } { n } ) ^ { n }$

Let $n = 5k$.

$\lim \limits_{5k\to\infty}\left(1+\frac{5}{5k}\right)^{5k}$

1. $\lim \limits _ { n \rightarrow \infty } ( 1 + \frac { 1 } { 2 n } ) ^ { n }$

Let $n = k/2$.