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: 7

Answer

FALSE

Work Step by Step

Ratio Test: $\lim\limits_{n \to +\infty}|\frac{a_{n}+1}{a_{n}}|=\lim\limits_{n \to +\infty}\frac{1}{(n+1)^{3}}\times \frac{n^{3}}{1}$ $=\lim\limits_{n \to +\infty}|\frac{1}{(1+1/n)^{3}}|$ $=\frac{1}{(1+1/\infty)^{3}}$ $=\frac{1}{(1+0)^{3}}$ $=1$ Ratio Test inconclusive when limit =1 . Hence, the statement is false.
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