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: 31



Work Step by Step

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. Re-arrange the given series as: $0.2777...=0.2 +0.07 +0.07(0.1) +0.07(0.1)^2 +....$ First term $a_1=0.07$ and Common ratio $r=0.1$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=0.2 +\dfrac{0.07}{1-0.1}=0.2 +\dfrac{7}{90}$ Hence, $S_n=\dfrac{18+7}{90}=\dfrac{5}{18}$
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.