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: 69

Answer

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.
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