Sequence and Limit

Calculus Level 1

If \(\{a_n\}\) is a sequence satisfying \(\displaystyle \lim_{n\rightarrow \infty}\frac{a_n}{n}=\frac{1}{3},\) what is \[\displaystyle \lim_{n\rightarrow \infty}\frac{\sqrt{9n^2+n}-n}{a_n}?\]

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