Answer
Converges to $\frac{\pi}{2}$
Work Step by Step
Given:$a_n=arctan(ln(n))$
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}arctan(ln(n))$
Now,
$\lim\limits_{n \to \infty}(ln(n))=\infty$
Therefore, $\lim\limits_{n \to \infty}arctan(ln(n))=\lim\limits_{n \to \infty}arctan(\infty)=\frac{\pi}{2}$
Hence, the sequence converges to $\frac{\pi}{2}$.
