Answer
Converges to $0$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} [\dfrac{(\ln n)^{200}}{n}]$
Since, $ \lim\limits_{n \to \infty} [\dfrac{(\ln n)^{200}}{n}]=\dfrac{\infty}{\infty}$
Need to apply L-Hospital's rule.
So, $\lim\limits_{n \to \infty} [\dfrac{(\ln n)^{200}}{n}]=\lim\limits_{n \to \infty} \dfrac{200 (\ln n)^{199}}{(n)(1)}]=\dfrac{\infty}{\infty}$
Again apply L-Hospital's rule.
we have $\lim\limits_{n \to \infty} \dfrac{200 !}{n}=0$
Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is Convergent and converges to $0$
