Answer
converges to $0$
Work Step by Step
As we know that $ \lim\limits_{n \to \dfrac{\pi}{2}} \tan x=\dfrac{\pi}{2}$ and $\lim\limits_{n \to \infty} \dfrac{1}{\sqrt n}=0$
Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{1}{\sqrt n}) \tan^{-1} n$
This implies that $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{1}{\sqrt n})(\tan^{-1} n)=(0) (\dfrac{\pi}{2})$
and $a_n=0$
Thus, {$a_n$} is Convergent and converges to $0$.
