Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 21

Answer

$\dfrac{1}{2}$

Work Step by Step

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. First term $a_1= \dfrac{2}{3}$ and Common ratio $r=\dfrac{-1}{3}$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{ \dfrac{2}{3}}{1-( \dfrac{-1}{3})}=\dfrac{ \dfrac{2}{3}}{1+ \dfrac{1}{3}}$ Hence, $S_n=\dfrac{1}{2}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.