Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 9 - Infinite Series - 9.2 Exercises: 8

Answer

diverges.

Work Step by Step

Th.9.6 Convergence of a Geometric Series: A geometric series with ratio $r$ diverges when $|r| \geq 1$. If $0 < |r| < 1$, then the series converges to the sum $\displaystyle \sum_{n=0}^{\infty}ar^{n}=\frac{a}{1-r},\quad 0 < |r| < 1$. ------------ $\displaystyle \sum_{n=0}^{\infty}4(-1.05)^{n} $is a geometric series, with $|r|=|-1.05|=1.05 > 1$ By Th.9.6, the series diverges.
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