Calculus (3rd Edition)

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

Chapter 11 - Infinite Series - 11.1 Sequences - Exercises - Page 538: 37



Work Step by Step

We have $$ \lim\limits_{n \to \infty}{c_n}=\lim\limits_{n \to \infty} 1.01^n=\infty.$$ Where we used the fact that $\lim_{x\to \infty } a^x=\infty$ when $|a|\gt 1$. Using Theorem 1, we see that the sequence $c_n$ diverges.
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