Calculus (3rd Edition)

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

Chapter 11 - Infinite Series - 11.2 Summing and Infinite Series - Preliminary Questions - Page 547: 5


The reasoning is not valid.

Work Step by Step

The reasoning is not valid. The student is using the divergence test to test for convergence. Just because the limit of the series tends toward zero, this does not imply convergence. The series can still diverge. On the other hand, if the limit was not zero, then we would know with certainty that it diverges.
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