Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.1 Sequences - 12.1 Assess Your Understanding - Page 807: 23



Work Step by Step

We are given the sequence: $\{t_n\}=\left\{\dfrac{(-1)^n}{(n+1)(n+2)}\right\}$ Determine the first 5 terms of the sequence by substituting 1, 2, 3, 4, 5 for $n$: $t_1=\dfrac{(-1)^n}{(n+1)(n+2)}=\dfrac{-1}{2\cdot 3}=-\dfrac{1}{6}$ $t_2=\dfrac{(-1)^n}{(n+1)(n+2)}=\dfrac{1}{3\cdot 4}=\dfrac{1}{12}$ $t_3=\dfrac{(-1)^n}{(n+1)(n+2)}=\dfrac{-1}{4\cdot 5}=-\dfrac{1}{20}$ $t_4=\dfrac{(-1)^n}{(n+1)(n+2)}=\dfrac{1}{5\cdot 6}=\dfrac{1}{30}$ $t_5=\dfrac{(-1)^n}{(n+1)(n+2)}=\dfrac{-1}{6\cdot 7}=-\dfrac{1}{42}$
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