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 488: 44


The limit does not exist (divergent).

Work Step by Step

Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} n\pi \cos (n \pi)$ Since, $\cos (n \pi)=\pm 1$; value depends on the value of $n$ Thus, $\lim\limits_{n \to \infty} n\pi \cos (n \pi)= n\pi (-1)^n$ Hence, the Limit Does Not Exist.
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