# Chapter 11 - 11.1 - Sequences and Series - 11.1 Exercises - Page 778: 90

(a) $\frac{26}{27}$ (b) $\frac{80}{81}$ (c) $\frac{242}{243}$

#### Work Step by Step

$\displaystyle \sum_{i=1}^{∞}2(\frac{1}{3})^i$ (a) $2(\frac{1}{3})^1+2(\frac{1}{3})^2+2(\frac{1}{3})^3=\frac{2}{3}+\frac{2}{9}+\frac{2}{27}=\frac{18+6+2}{27}=\frac{26}{27}$ (b) $2(\frac{1}{3})^1+2(\frac{1}{3})^2+2(\frac{1}{3})^3+2(\frac{1}{3})^4=\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+\frac{2}{81}=\frac{54+18+6+2}{81}=\frac{80}{81}$ (c) $2(\frac{1}{3})^1+2(\frac{1}{3})^2+2(\frac{1}{3})^3+2(\frac{1}{3})^4+2(\frac{1}{3})^5=\frac{2}{3}+\frac{2}{9}+\frac{2}{27}+\frac{2}{81}+\frac{2}{243}=\frac{162+54+18+6+2}{243}=\frac{242}{243}$

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.