University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.1 - Sequences - Exercises - Page 488: 85


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 $0$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.