I need help with the following limit: $$\lim\limits_{n\to\infty} \left(\frac{\left(1+\frac{1}{n}\right)^{n}}{e}\right)^{n}$$
I tried using $\ln$, taking out the $n$, writing it as $\frac{1}{n}$ in the denominator and performing l'Hôpital (and then using the exponent to get the limit). But for some reason I'm not reaching the correct limit. I would greatly appreciate if someone could show me steps for solving this limit. Thank you.