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: 42

Answer

$S_{1}=-1$ $S_{2}=0$ $S_{3}=-1$ $S_{4}=0$ $S_{5}=-1$ $S_{6}=0$

Work Step by Step

We are given: $-1, 1, -1, 1$ ... We notice that the terms alternate between $-1$ and $1$: $a_{1}=-1=(-1)^1$ $a_{2}=1=(-1)^2$ $a_{3}=-1=(-1)^3$ $a_{4}=1=(-1)^4$ Therefore: $a_{n}=(-1)^{n}$ So: $a_{5}=-1$ $a_{6}=1$ We find the partial sums: $S_{1}=-1$ $S_{2}=-1+1=0$ $S_{3}=0-1=-1$ $S_{4}=-1+1=0$ $S_{5}=0-1=-1$ $S_{6}=-1+1=0$
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