College Algebra 7th Edition

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

Chapter 8, Sequences and Series - Section 8.1 - Sequences and Summation Notation - 8.1 Exercises: 18

Answer

$a_1=1$ $a_2=\frac{1}{2}$ $a_3=\frac{2}{3}$ $a_4=\frac{3}{5}$ $a_{5}=\frac{5}{8}$

Work Step by Step

We are given: $a_{n}=\frac{1}{1+a_{n-1}}$ and $a_1=1$ We evaluate: $a_2=\frac{1}{1+a_{1}}=\frac{1}{1+1}=\frac{1}{2}$ $a_3=\frac{1}{1+a_{2}}=\frac{1}{1+\frac{1}{2}}=\frac{2}{3}$ $a_4=\frac{1}{1+a_{3}}=\frac{1}{1+\frac{2}{3}}=\frac{3}{5}$ $a_{5}=\frac{1}{1+a_{4}}=\frac{1}{1+\frac{3}{5}}=\frac{5}{8}$
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