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: 6

Answer

Diverges

Work Step by Step

Consider $u_n=(-1)^{n+1}\dfrac{n^2+5}{ n^2+4}$ Now $\lim\limits_{n \to \infty} u_n=\dfrac{n^2+5}{ n^2+4}=1$ $\lim\limits_{n \to \infty} (-1)^{n+1}\dfrac{n^2+5}{ n^2+4}=DNE$ Thus the series diverges by the nth Term Test for Divergence.
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