Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Practice Exercises - Page 636: 32



Work Step by Step

Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{\ln n}{\ln (\ln n)}$ But, $\lim\limits_{n \to \infty} \dfrac{\ln n}{\ln (\ln n)}=\dfrac{\infty}{\infty}$ Apply L-hospital's rule such that $\lim\limits_{x \to k}\dfrac{p(x)}{q(x)}=\lim\limits_{x \to k}\dfrac{p'(x)}{q'(x)}$ $\implies \lim\limits_{n \to \infty}\dfrac{n \ln (n)}{n}=\infty$ Hence, the series diverges.
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.