Answer
False.
Work Step by Step
Just because a sequence converges doesn't mean that the series diverges. For example, the sequence $a_n=2$ converges at 2, but a sum of infinite $2$s is infinity, making the series diverge.
Calculus, 10th Edition (Anton)
by Anton, Howard
Published by
Wiley
ISBN 10:
0-47064-772-8
ISBN 13:
978-0-47064-772-1
Chapter 9 - Infinite Series - 9.3 Infinite Series - Exercises Set 9.3 - Page 622: 17
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