Answer
(a) $\frac{7}{8}$
(b) $\frac{15}{16}$
(c) $\frac{31}{32}$
Work Step by Step
$\displaystyle \sum_{i=1}^{∞}(\frac{1}{2})^i$
(a) $(\frac{1}{2})^1+(\frac{1}{2})^2+(\frac{1}{2})^3=\frac{1}{2}+\frac{1}{8}+\frac{1}{8}=\frac{7}{8}$
(b) $(\frac{1}{2})^1+(\frac{1}{2})^2+(\frac{1}{2})^3+(\frac{1}{2})^4=\frac{1}{2}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}=\frac{15}{16}$
(c) $(\frac{1}{2})^1+(\frac{1}{2})^2+(\frac{1}{2})^3+(\frac{1}{2})^4+(\frac{1}{2})^5=\frac{1}{2}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}=\frac{31}{32}$
