## anonymous one year ago evaluate limit ( sqrt(n^2+n) - n )

1. P0sitr0n

assuming we are taking the limit to infinity, simply multiply the top and the bottom by the conjugate of the numerator, i.e. $(\sqrt{n^2+n}+n)$ Then this will allow you to simplify your fraction up to $\lim_{n \rightarrow \infty}\frac{n}{\sqrt{n^2+n}+n}$ Now factor and simplify

2. anonymous

I have reached to as limit n goes to infinity (n/sqrt(n^2+n) +n)

3. anonymous

Dividing by n ?

4. P0sitr0n

ok good. Now what you can do is factor out the n^2 out of the square root, which will give you $n(\sqrt{1+\frac{1}{n}}+1)$ in the bottom

5. P0sitr0n

yeah, then you cancel both n, and are left with an expression that you can evaluate

6. anonymous

Canceling from above ?

7. anonymous

Yes I get it now

8. anonymous

Thank you