Originally Posted by

**entropyslave** Hi there,

I am trying to see why this function goes to zero at the limit of large n (for constant a):

$\displaystyle \frac{2}{a}(\sqrt{n}\sqrt{n+a}-2n-a)$

With some factoring out, I've arrived at this:

$\displaystyle \frac{2n}{a}(\sqrt{1+\frac{a}{n}}-1-\frac{a}{2n})$

Where the first (root) term in the bracket should go to 1, and the last to 0, thus the bracket should approach zero in the limit. However, for some reason I don't feel quite comfortable with my method and reasoning. Don't I have to worry about the rate the two terms of the product approach their respective limits? Is there a better way to express the function to make this nuance clear?