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: 23

Answer

The first five terms are: $t_1 = -\dfrac{1}{6}; \\t_2= \dfrac{1}{12}; \\t_3= -\dfrac{1}{20}; \\t_4= \dfrac{1}{30}; \\t_5= -\dfrac{1}{42}$

Work Step by Step

Substitute $n=1, 2, 3, 4, 5$ to obtain: $t_1 = \dfrac{(-1)^1}{(1+1)(1+2)}=\dfrac{-1}{2(3)}=-\dfrac{1}{6}; \\t_2= \dfrac{(-1)^2}{(2+1)(2+2)}=\dfrac{1}{3(4)}=\dfrac{1}{12}; \\t_3= \dfrac{(-1)^3}{(3+1)(3+2)}=\dfrac{-1}{4(5)}=-\dfrac{1}{20}; \\t_4= \dfrac{(-1)^4}{(4+1)(4+2)}=\dfrac{1}{5(6)}=\dfrac{1}{30}; \\t_5= \dfrac{(-1)^5}{(5+1)(5+2)}=\dfrac{-1}{6(7)}=-\dfrac{1}{42}$
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