University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 9 - Section 9.3 - The Integral Test - Exercises - Page 504: 4



Work Step by Step

Consider $f(x)=\dfrac{1}{x+4}$. This is positive, continuous and decreasing for $x \geq 1$ Now, take the integral test to find the convergence and divergence for the sequence. We have $\int_1^\infty \dfrac{1}{x+4} dx= \lim\limits_{a \to \infty} \int_1^a \dfrac{1}{x+4} dx$ or, $ \lim\limits_{a \to \infty} [\ln |x+4|]_1^a=\lim\limits_{a \to \infty} [\ln |a+4|-\ln 5]= \infty$ Hence, the sequence $\Sigma_{n=1}^\infty \dfrac{1}{n+4}$ is Divergent
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.