College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.1 - Sequences - 9.1 Assess Your Understanding: 21

Answer

The first five terms are: $s_1 = \dfrac{1}{2}; \\s_2= \dfrac{2}{5}; \\s_3= \dfrac{2}{7}; \\s_4= \dfrac{8}{41}; \\s_5= \dfrac{8}{61}$

Work Step by Step

Substitute $n=1, 2, 3, 4, 5$ to obtain: $s_1 = \dfrac{2^1}{3^1+1}=\dfrac{2}{4} = \dfrac{1}{2}; \\s_2= \dfrac{2^2}{3^2+1}=\dfrac{4}{10} = \dfrac{2}{5}; \\s_3= \dfrac{2^3}{3^3+1}=\dfrac{8}{28} = \dfrac{2}{7}; \\s_4= \dfrac{2^4}{3^4+1}=\dfrac{16}{82} = \dfrac{8}{41}; \\s_5= \dfrac{2^5}{3^5+1}=\dfrac{32}{244} = \dfrac{8}{61}$
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