Limit of a polynomic-exponential sequence I have to calculate the following limit:
$$L=\lim \limits_{n \to \infty} -(n-n^{n/(1+n)})$$
I get the indeterminate form $\infty - \infty$ and I don't know how to follow.  Any idea?
Thank you very much.

HINT : 
$$n - n^{n/1+n} = n - n^{1+1/n} = n(1 - n^{1/n}) = \frac{1 - n^{1/n}}{1/n}$$
Now use L'Hôpital's rule.
