Chapter 11 - 11.3 - Geometric Sequences and Series - 11.3 Exercises - Page 796: 71

$S=\frac{2}{3}$

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