# How do you determine whether the infinite sequence a_n=e^(1/n) converges or diverges?

Oct 1, 2014

Let us evaluate the limit.

${\lim}_{n \to \infty} {a}_{n} = {\lim}_{n \to \infty} {e}^{\frac{1}{n}}$

by squeeze the limit into the exponent,

$= {e}^{{\lim}_{n \to \infty} \frac{1}{n}} = {e}^{\frac{1}{\infty}} = {e}^{0} = 1$

Hence, the sequence converges to $1$.