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 - Chapter Review - Review Exercises - Page 859: 22



Work Step by Step

An infinite geometric series is said to converge if and only if $|r|\lt1$, and their sum can be expressed as: $a_n=\dfrac{a_1}{1-r}$ where $a_1=\ First \ Term$ and $r$ is the common ratio of the quotient of two consecutive terms: So, $r=\dfrac{a_2}{a_1}=\dfrac{1}{3}=\dfrac{1}{3}; |\dfrac{1}{3}|\lt1$ and $a_1=3$ Therfore, the series converges and its sum is: $a_n=\dfrac{3}{1-\dfrac{1}{3}}=\dfrac{9}{2}$
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