Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 12 - Section 12.1 - Sequences and Summation Notation - 12.1 Exercises - Page 850: 18


$a_{1}=1$, $a_{2}=\displaystyle \frac{1}{2}$, $a_{3}=\displaystyle \frac{2}{3}$, $a_{4}=\displaystyle \frac{3}{5}$, $a_{5}=\displaystyle \frac{5}{8}$

Work Step by Step

$a_{1}=1$, $.\displaystyle \qquad a_{n}=\frac{1}{1+a_{n-1}}$ $a_{2}=\displaystyle \frac{1}{1+1}=\frac{1}{2}$ $a_{3}=\displaystyle \frac{1}{1+\frac{1}{2}}=\frac{1}{\frac{2+1}{2}}=\frac{2}{3}$ $a_{4}=\displaystyle \frac{1}{1+\frac{2}{3}}=\frac{1}{\frac{3+2}{3}}=\frac{3}{5}$ $a_{5}=\displaystyle \frac{1}{1+\frac{3}{5}}=\frac{1}{\frac{5+3}{5}}=\frac{5}{8}$
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