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.

Since you received good answers, if I may, I suggest you plot on the same graph the two following functions  $$f(n)= -(n-n^{n/(1+n)})$$ $$g(n)=-\log(n)$$ You will probably be amazed to see how close they are (even for $n$ around $100$).  
In fact, but this is off topic, what you could show is that, for large values of $n$,$$f(n) \simeq \log \left(\frac{1}{n}\right)+\frac{\left(\log \left(\frac{1}{n}\right)-2\right)
   \log \left(\frac{1}{n}\right)}{2 n}+O\left(\left(\frac{1}{n}\right)^2\right)$$ 
