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 735: 29


The given series is divergent.

Work Step by Step

$\Sigma^{\infty}_{n=1} \frac{n-1}{3n-1}$ $\lim\limits_{n \to \infty}a_{n} = \lim\limits_{n \to \infty}(\frac{n-1}{3n-1})$ $= \lim\limits_{n \to \infty} (\frac{1-\frac{1}{n}}{3-\frac{1}{n}})$ $= \frac{1}{3} \ne 0$ The given series diverges since $\lim\limits_{n \to \infty}a_{n} \ne 0$. The series $\Sigma^{\infty}_{n=1} a_{n}$ is divergent.
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