University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 498: 65

Answer

Diverges

Work Step by Step

Here, we have: $ s_n=(\ln (1) - \ln (2))+(\ln (2) - \ln (3))+.......+(\ln (n) - \ln (n+1))=-\ln (n+1)$ Thus, we have the sum $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} -\ln (n+1)=-\infty$ This shows that the sequence of partial sums diverges and thus the series also diverges.
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