Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 796: 70

$S=8$

$\displaystyle \sum_{n=0}^{∞}2(\frac{3}{4})^n=2(\frac{3}{4})^0+2(\frac{3}{4})^1+2(\frac{3}{4})^2+...$ $a_1=2(\frac{3}{4})^0=2$ $r=\frac{a_2}{a_1}=\frac{2(\frac{3}{4})^1}{2(\frac{3}{4})^0}=\frac{3}{4}$ $S=\frac{a_1}{1-r}=\frac{2}{1-\frac{3}{4}}=\frac{2}{\frac{1}{4}}=8$