Find the limit:
$\displaystyle \lim\limits_{n\to\infty}(\frac{(1+\frac{1}{n})^n}{ e})^n$
the answer is $\displaystyle \frac{1}{\sqrt{e}}$ so i guess we should get something like $\displaystyle \lim\limits_{n\to\infty}(1-\frac{1}{2n})$.. but dont know what to do with double n and exp. also:
$\displaystyle \lim\limits_{n\to\infty}(\prod\limits_{k=1}^{n}\fr ac{k}{k+n})^{e^{\frac{1999}{n}}-1}$ so thats $\displaystyle \lim\limits_{n\to\infty}(\frac{n!^2}{2n!})^{e^{\fr ac{1999}{n}}-1}$ but again, what to do with exp?