## Calculus 8th Edition

Published by Cengage

# Chapter 11 - Infinite Sequences and Series - Review - True-False Quiz: 15

FALSE

#### Work Step by Step

Consider $a_{n}=(-1)^n$ and $b_{n}=(-1)^{n+1}$ (Both diverge) Then $a_{n}b_{n}=(-1)^n\times (-1)^{n+1}= (-1)^{2n+1}=-1$ Since, only one of them is always negative for any $n$ so, It converges. Hence, the statement is false.

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