# Limit

Calculus Level pending

$\lim_{n\to \infty} \left(\sqrt{\left\lfloor {\left( 9n-\frac{1}{6} \right)^2}\right\rfloor} - (9n-1)\right) = \frac{a}{b}$

Suppose $$a$$ and $$b$$ are positive integers and $$\gcd(a,b) =1$$. Find the value of $$a+b$$.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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