Give me hints for evaluating this limit Evaluate this limit:
$$\lim_{n\to\infty}{\left\{\left(1+\frac{1}{n}\right)^n-\left(1+\frac{1}{n}\right)\right\}}^{-n}$$
Please give me some hints. If you provide a complete answer instead, please include a spoiler tag. 

Hint.
$$\lim_{n\to\infty}\left(1+\frac{x}{n}\right)^n=e^x=\exp(x)$$
From here on you can easily conclude the result as you mentioned in the comments of your post.
