Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 9 - Infinite Series - 9.1 Sequences - Exercises Set 9.1 - Page 606: 26


General term: $$(-1)^{n}n$$ This sequence does not converges.

Work Step by Step

Each term of the sequence is $n$ with alternating sign. This suggests that $(-1)^n$ term is multiplied with each term of the sequence. Thus, general term: $$(-1)^{n}n$$ As $n\to\infty$, the general term keep on increasing in magnitude, thus the limit doesn't exist. Thus, the sequence does not converges.
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