What is the limit of (1+1/x)^x as x approaches infinity?

May 28, 2017

${\lim}_{\text{x->oo}} {\left(1 + \frac{1}{x}\right)}^{x} = e \approx 2.71828$

Explanation:

Consider the standard limit: ${\lim}_{\text{x->oo}} {\left(1 + \frac{k}{x}\right)}^{x} = {e}^{k}$

In the example $k = 1$

Hence, ${\lim}_{\text{x->oo}} {\left(1 + \frac{1}{x}\right)}^{x} = {e}^{1}$

$= e \approx 2.71828$