Hi,

I'm trying to prove the following limit

$\displaystyle \sqrt{x(x+1)}-x = \frac{1}{2}$ as x approaches infinity.

I'm getting stuck on the expansion of

$\displaystyle x\sqrt{1+1/x}$

I know that it's supposed to be

$\displaystyle x(1+\frac{1}{2x}-\frac{1}{8x^2} +.....)$

but I can't work out the series.

Can anyone help?