Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.5 The Ratio and Root Tests and Strategies for Choosing Tests - Exercises - Page 568: 43


The series $\sum_{n=1}^{\infty} \frac{2^{n}+4^{n}}{7^{n}}$ converges.

Work Step by Step

In the series $\sum_{n=1}^{\infty} \frac{2^{n}+4^{n}}{7^{n}}$, we have the series $$\sum_{n=1}^{\infty} \frac{2^{n} }{7^{n}}=\sum_{n=1}^{\infty} (\frac{2 }{7 })^n$$ which is a convergent geometric series with $r=2/7\lt 1$. Also, the series $$\sum_{n=1}^{\infty} \frac{4^{n} }{7^{n}}=\sum_{n=1}^{\infty} (\frac{4 }{7 })^n$$ is a convergent geometric series with $r=4/7\lt 1$. Hence, the series $\sum_{n=1}^{\infty} \frac{2^{n}+4^{n}}{7^{n}}$ converges.
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.