University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.6 - Alternating Series and Conditional Convergence - Exercises - Page 521: 37


Absolutely Convergent

Work Step by Step

We need to apply the Root Test to the series. $L=\lim\limits_{n \to \infty} |a_n|^{1/n}=\lim\limits_{n \to \infty} |\dfrac{(-1)^n(n+1)^n}{(2n)^n}|=\Sigma_{n=1}^{\infty} \dfrac{n+1}{2n}$ or, $=\Sigma_{n=1}^{\infty} \dfrac{n/n+1/n}{2n/n}$ So, $=\dfrac{1}{2} \lt 1$ Thus, the series is Absolutely Convergent by the ratio test.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.