Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 32


$\{a_n\}=n ^{(-1)^{n+1}}$

Work Step by Step

We notice that the sequence always contains a number that starts with $1$ and increases by $1$ each time ($1,2,3,4,5...$). This value is sometimes in the numerator (to the power of $1$) and sometimes in the denominator (to the power of $-1$), depending on whether the term number is even or odd. So, we can determine the pattern as $$\{a_n\}=n ^{(-1)^{n+1}}$$
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