Limit with criteria $\lim_{n \to \infty}n \cdot \left [ \frac1e \left (1+\frac{1}{n+1} \right )^{n+1}-1 \right ]$
How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?