Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 796: 69

$S=2$

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