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: 28

Answer

$\{a_n\}=\dfrac{1}{n(n+1)}$ .

Work Step by Step

We notice from the sequence that the numerator is constant at $1$. The denominator shows the pattern of $1*2$, $2*3$, $3*4$, etc. Thus, in general the denominator has the pattern of $n(n+1)$. So, we determine the sequence pattern as $$\{a_n\}=\dfrac{1}{n(n+1)}$$
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