Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 537: 26


The sequence $r_n$ diverges.

Work Step by Step

Since we have $$\lim_{n\to \infty}r_n=\lim_{n\to \infty} \ln n -\ln (n^2+1) =\lim_{n\to \infty}\ln\left(\frac{n}{n^2+1}\right)\\ =\ln \lim_{n\to \infty}\frac{1/n}{1+(1/n^2)}=\ln 0=-\infty,$$ then the sequence $r_n$ diverges.
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