Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 9 - Infinite Series - 9.1 Sequences - Exercises Set 9.1 - Page 605: 8


first five terms: $\frac{1}{3}, \frac{4}{5}, \frac{9}{7}, \frac{16}{9}, \frac{25}{11}$, diverges

Work Step by Step

To find the first five terms of the sequence, put the values $1,2,3,4,5$ into the function $a_n=\frac{n}{n+2}$. To find if the sequence converges, find the limit as n approaches positive infinity. This leaves $$\lim\limits_{n \to \infty} \frac{n^2}{2n+1}$$ Since the highest degree in the numerator is higher than the highest degree in the denominator, the limit is infinity and the sequence diverges.
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.