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: 35



Work Step by Step

We have $$ \lim\limits_{n \to \infty}{a_n}=\lim\limits_{n \to \infty} 10+(-1/9)^n=10.$$ Where we used the fact that $\lim_{x\to \infty} a^x=0$ when $|a|\lt 1$. Using Theorem 1, we get that the sequence $a_n$ converges to $10$.
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