Answer
S is larger than $S_{100}$.
Work Step by Step
In this case, $S$ is an alternating series and hence $$|S-S_{100}|\lt a_{101}=10^{-3}.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 11 - Infinite Series - 11.4 Absolute and Conditional Convergence - Preliminary Questions - Page 562: 4
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