lim [ ((1+5/n)^n) / e^5 ] ^n hint: use lny
Taking into consideration that we have:
$\displaystyle \color{blue}\boxed{\lim_{n \to \infty} \left(1+\frac {a}{n}\right)^{bn} = e^{ab}}$
so we have:
$\displaystyle \lim_{n\to\infty}\left(\frac{\left(1+\frac{5}{n}\r ight)^n}{e^5}\right)^n=\lim_{n\to\infty}\left(\fra c{e^5}{e^5}\right)^n$ = 1