Briefly explain what is wrong with the following attempt to determine if the sequence $a_n=e^{\frac{n+1}{n}}$ converges or diverges.

Check $\underset{n}{lim}{a}_n=\underset{n}{lim}{e}^{\frac{n+1}{n}}$

As $n$ goes to $,\frac{n+1}{n}$ goes to $1,$ so

$=\underset{n}{lim}{e}^{\frac{n+1}{n}}=e^1=e$

Since $\underset{n}{lim}{a}_{n}0,$ the sequence $a_n$ diverges.