Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.1 An Overview - 8.1 Exercises: 70

Answer

a) $-1, 1, -1, 1$ b) Limit does not exist

Work Step by Step

$$\sum_{k=1}^{\infty} cos(\pi k)$$ Part A) $a_1 = cos(\pi (1)) = -1$ $a_2 = cos(\pi (2)) = 1$ $a_3 = cos(\pi (3)) = -1$ $a_4 = cos(\pi (4)) = 1$ First four terms: $-1, 1, -1, 1$ Part B) The sequence does not seem to converge, since the term values are simply alternating between $1$ and $-1$.
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