## Algebra 2 (1st Edition)

Published by McDougal Littell

# Chapter 12 Sequences and Series - 12.4 Find Sums of Infinite Geometric Series - 12.4 Exercises - Skill Practice - Page 823: 28

#### Answer

$\dfrac{3200}{99}$

#### Work Step by Step

Here, we have $a_n= a_1 r^{n-1}$ for the Geometric series. Re-arrange the given series as: $32.32323232...=32 +32 (0.01) +32(0.01)^2 +....$ First term $a_1=0.625$ and Common ratio $r=0.01$ The sum of an infinite Geometric Series can be found using: $S_n=\dfrac{a_1}{1-r}$ Thus, $S_n=\dfrac{32}{1-0.01}$ Hence, $S_n=\dfrac{3200}{99}$

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.