College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 607: 69


Yes, harmonic.

Work Step by Step

We are given: $1, \frac{3}{5}, \frac{3}{7}, \frac{1}{3}$ ... $\frac{1}{1}, \frac{3}{5}, \frac{3}{7}, \frac{1}{3}$ ... We take the reciprocals of the terms: $\frac{1}{1}, \frac{5}{3}, \frac{7}{3}, \frac{3}{1}$ ... $1, 1.\overline 6, 2.\overline 3, 3$ We see that the terms increase by $0.6\overline 6$, or $\frac{2}{3}$. Thus the reciprocals form an arithmetic sequence, which implies that the original sequence is harmonic.
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.