Calculus 8th Edition

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

Chapter 11 - Infinite Sequences and Series - 11.2 Series - 11.2 Exercises - Page 758: 82


$\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges.

Work Step by Step

If $\Sigma^{\infty}_{ n=1} a_{n}$ converges, then by divergence test : $\lim\limits_{n \to \infty}a_{n}=0$ Which in turn implies that $\lim\limits_{n \to \infty} \frac{1}{a_{n}} \ne 0$ As per the divergence test we can conclude that $\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges. Hence, $\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges.
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