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: 51


The sequence $c_n$ converges to $ \ln \left(\frac{2 }{3 }\right).$

Work Step by Step

We have $$\lim_{n\to \infty}c_n=\lim_{n\to \infty} \ln \left(\frac{2 n+1}{3 n+4}\right) \\ =\ln \lim_{n\to \infty} \left(\frac{2 n+1}{3 n+4}\right)=\ln \lim_{n\to \infty} \left(\frac{2 +1/n}{3 +4/n}\right)\\ = \ln \left(\frac{2 }{3 }\right).$$ Hence, by Theorem 1, the sequence $c_n$ converges to $ \ln \left(\frac{2 }{3 }\right).$
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