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: 20

Answer

The first five terms are: $d_1 = 1; \\d_2= -\frac{2}{3}; \\d_3= \frac{3}{5}; \\d_4= -\frac{4}{7}; \\d_5= \frac{5}{9}$

Work Step by Step

Substitute $n=1, 2, 3, 4, 5$ to obtain: $d_1 = (-1)^{1-1}\left(\dfrac{1}{2(1)-1}\right)=(-1)^0(\frac{1}{1})=1(1)=1; \\d_2= (-1)^{2-1}\left(\dfrac{2}{2(2)-1}\right)=(-1)^1(\frac{2}{3})=-1(\frac{2}{3})=-\frac{2}{3}; \\d_3= (-1)^{3-1}\left(\dfrac{3}{2(3)-1}\right)=(-1)^2(\frac{3}{5})=1(\frac{3}{5})=\frac{3}{5}; \\d_4= (-1)^{4-1}\left(\dfrac{4}{2(4)-1}\right)=(-1)^3(\frac{4}{7})=-1(\frac{4}{7})=-\frac{4}{7}; \\d_5= (-1)^{5-1}\left(\dfrac{5}{2(5)-1}\right)=(-1)^4(\frac{5}{9})=1(\frac{5}{9})=\frac{5}{9}$
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