Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - Review - True-False Quiz - Page 825: 18



Work Step by Step

$\lim\limits_{n \to \infty}\frac{a_{{n+1}}}{a_{n}}\lt 1$ For this to be true , $a_{n}$ must be decreasing. $a_{n+1}\lt a_{n}$ and since $a_{n}=0$, then $\lim\limits_{n \to \infty}a_{n}=0$ must be true because while $a_{n}$ is decreasing, it cannot go to exactly or below $0$. Hence, the statement is true.
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