Question

evaluate limit ( sqrt(n^2+n) - n )

Answer 1

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

Answer 2

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

Answer 3

Dividing by n ?

Answer 4

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

Answer 5

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

Answer 6

Canceling from above ?

Answer 7

Yes I get it now

Answer 8

Thank you