Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 12 - Section 12.2 - Arithmetic Sequences - 12.2 Exercises - Page 857: 69


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The given sequence can be rewritten (for easier pattern recognition) as $\displaystyle \frac{3}{3},\ \displaystyle \frac{3}{5},\ \displaystyle \frac{3}{7},\ \displaystyle \frac{3}{9},\ \displaystyle \frac{3}{11},\ ...$ The reciprocals form a sequence $\displaystyle \frac{3}{3},\ \displaystyle \frac{5}{3},\ \displaystyle \frac{7}{3},\ \displaystyle \frac{9}{3},\ \displaystyle \frac{11}{3},\ ...$ which we recognize to be arithmetic, because it has a common difference, $d=\displaystyle \frac{2}{3}.$ The reciprocals form an arithmetic sequence, so the original sequence is harmonic.
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