Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 11 - Infinite Sequences and Series - Review - Exercises - Page 825: 2



Work Step by Step

A sequence is said to be converged if and only if $\lim\limits_{n \to \infty}a_{n}$ is a finite constant. $\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}\frac{9^{n+1}}{10^{n}}$ $=\lim\limits_{n \to \infty}9\times (\frac{9}{10})^{n}$ Since, $\lim\limits_{n \to \infty}a^{n}=0$ for $|a|\lt 1$ Thus, $\lim\limits_{n \to \infty}9\times (\frac{9}{10})^{n}=9\times 0=0$ Hence, the given sequence converges to $0$.
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