Answer
Converges to $\dfrac{\pi}{2}$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} tan^{-1} n$
Since, $ \lim\limits_{n \to \dfrac{\pi}{2}} \tan x=\dfrac{\pi}{2}$
So, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} tan^{-1} n=\dfrac{\pi}{2}$
Hence, $\lim\limits_{n \to \infty} a_n=\dfrac{\pi}{2}$ and {$a_n$} is Convergent and converges to $\dfrac{\pi}{2}$
