Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 11 - Infinite Sequences and Series - 11.2 Exercises - Page 737: 80

Answer

$\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ 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 $\lim\limits_{n \to \infty} \frac{1}{a_{n}} \ne 0$ By the divergence test we can say that $\Sigma^{\infty}_{ n=1} \frac{1}{a_{n}}$ diverges.
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