# Math Help - Calculate this limit

1. ## Calculate this limit

Need help with this limit please

$\lim{\sqrt{n^2+n}-n}$
n-> $\infty$

I know the answer is 1/2

2. Originally Posted by dlbsd
Need help with this limit please

$\lim{\sqrt{n^2+n}-n}$
n-> $\infty$

I know the answer is 1/2
On rationalising the numerator

$\lim_{n\to \infty}\frac{n}{\sqrt{n^2+n}+n}=\lim_{n\to \infty}\frac{1}{\sqrt{1+\frac{1}{n}}+1}=\frac{1}{1 +1}=\frac{1}{2}$