University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.1 - Sequences - Exercises - Page 489: 120

Answer

The sequence is convergent.

Work Step by Step

By the definition of the sequence, $x_{n+1}$ is the greater of "$x_{n}$ and another number". So, $x_{n+1}$ is never smaller than $x_{n}$. The sequence is monotonic (nondecreasing). Since every term is "$\cos$(some number)", the sequence is bounded, below by -1, and above by 1. By Th.6, the sequence is convergent.
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