Answer
$\displaystyle \sum_{i=1}^{4}(\frac{1}{2})^i=\frac{15}{16}$
Work Step by Step
$\displaystyle \sum_{i=1}^{4}(\frac{1}{2})^i=\displaystyle \sum_{i=1}^{4}\frac{1}{2}(\frac{1}{2})^{i-1}$
$a_1=\frac{1}{2}$
$r=\frac{1}{2}$
$S_n=a_1(\frac{1-r^n}{1-r})$
$S_4=\frac{1}{2}(\frac{1-(\frac{1}{2})^4}{1-\frac{1}{2}})=(\frac{1}{2})\frac{1-\frac{1}{16}}{\frac{1}{2}}=(\frac{1}{2})\frac{\frac{15}{16}}{\frac{1}{2}}=\frac{15}{16}$
