How to find $\lim_{n\to \infty} (\frac {n}{\sqrt{n^2+n}+\sqrt{n}})$? I am trying to solve this : $\lim_{n\to \infty} (\frac {n}{\sqrt{n^2+n}+\sqrt{n}})$ but I always end up with $\frac {\infty}{\infty}$ which is undefined
I tried for eg $$\lim_{n\to \infty} (\frac {n}{\sqrt{n^2+n}+\sqrt{n}}) (\frac {\sqrt{n^2+n}-\sqrt{n}}{\sqrt{n^2+n}-\sqrt{n}})$$
which resulted in:
$$\lim_{n\to \infty} \frac {n^2(\sqrt{1+\frac1n}-(\frac 1n)^\frac12)}{n^2}$$
but I cannot seem to find any other solutions
Thanks for help

You are almost done indeed 
$$\lim_{n\to \infty} \frac {n^2(\sqrt{1+\frac1n}-(\frac 1n)^\frac12)}{n^2}= \frac {(\sqrt{1+0}-(0)^\frac12)}{1}$$
