# The limit floored me

Calculus Level 4

$\displaystyle \lim_{n \to \infty} \left( \sqrt{n^2+n+1}-\left\lfloor \sqrt{ n^2+n+1 } \right \rfloor \right)=\ ?$

Take the limit over integer values of $$n$$.

Note: $$\lfloor .. \rfloor$$ represents Floor Function.