Answer
converges to $-2$
Work Step by Step
Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{1}{\sqrt {n^2-n}-\sqrt {n^2+n}}$
This can be re-written as: $\lim\limits_{n \to \infty} (\dfrac{1}{\sqrt {n^2-n}-\sqrt {n^2+n}}) (\dfrac{\sqrt {n^2-n}-\sqrt {n^2+n}}{\sqrt {n^2-n}-\sqrt {n^2+n}})=\lim\limits_{n \to \infty} \dfrac{\sqrt {n^2-1}+\sqrt {n^2+n}}{-(1+n)}[\dfrac{\dfrac{1}{n}}{\dfrac{1}{n}}]=-2$
Thus, {$a_n$} is Convergent and converges to $-2$.
