Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.3 Convergence of Series with Positive Terms - Exercises - Page 557: 55


The series $\sum_{n=5}^{\infty} (4/5)^{-n}$ diverges.

Work Step by Step

We have $$ \lim_{n\to \infty} (4/5)^{-n}=\lim_{n\to \infty} (5/4)^{n}=\infty.$$ Where we used the fact that $5/4\gt 1$. Hence, the series $\sum_{n=5}^{\infty} (4/5)^{-n}$ diverges.
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