# Interesting LImit to solve

$$\lim_{n\to infinity}{{(\sqrt{n^{2}+n+1}})-[{(\sqrt{n^{2}+n+1}})]}$$ wer [.] is GIF
how will u solve this one

For very large n, $n^2$ 'dominates' lower powers so that is asymptotic to $n- [n]$. And that has no limit.