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

Published by Pearson

Chapter 11 - Sequences; Induction; the Binomial Theorem - Chapter Review - Review Exercises - Page 859: 25

Answer

Converges; $8$

Work Step by Step

An infinite geometric series is said to converge if and only if $|r|\lt1$, and diverges when $|r| \gt 1$. The sum of a geometric series 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: Since, $a_1=4$ and $r=\dfrac{a_2}{a_1}=\dfrac{1}{2}$ Because $r= |\dfrac{1}{2}| \lt1$ Therefore, the series converges and its sum is equal to: $a_n=\dfrac{4}{1-\dfrac{1}{2}}=8$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.