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 538: 48



Work Step by Step

We have $$\lim_{n\to \infty}d_n=\lim_{n\to \infty}\ln(n^2+4)-\ln(n^2-1)\\ =\lim_{n\to \infty}\ln\frac{n^2+4}{n^2-1}=\ln 1=0.$$ Hence, by Theorem 1, the sequence $d_n$ converges to $0$.
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