$\lim_{n\rightarrow\infty}n\left[1-\left(1+\frac{1}{n}\right)^{e}\right]$
I tried playing around with the $\lim_{n\rightarrow\infty}n(1-\frac{1}{n})^n$ = $\frac{1}{e}$ identity but I can't really tell you where I'm headed with that one.
My gut keeps telling me the answer is infinity but my gut hasn't passed me an exam in years.
Some help would be nice.