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: 38

Answer

$a_{n}=n^{(-1)^{n+1}}$

Work Step by Step

We are given: $1, \frac{1}{2}, 3, \frac{1}{4}, 5, \frac{1}{6}$ ... We notice that the terms are integers raised to positive or negative $1$ (alternating). We find the pattern: $a_1=1^1$ $a_2=2^{-1}$ $a_3=3^{1}$ $a_4=4^{-1}$ $a_5=5^{1}$ Therefore: $a_{n}=n^{(-1)^{n+1}}$
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