## University Calculus: Early Transcendentals (3rd Edition)

Converges to $0$
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 $0$