Answer
False
Work Step by Step
As a counter- example, the sequences given by
$T_n = n$ and
$U_n = -n$
both diverge to $+\infty$ and $-\infty$ respectively but their sum
$S_n = T_n +U_n = n + (-n) = 0$
clearly converges to 0
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 9 - Inifnite Series - 9.1 Exercises - Page 594: 82
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