Math

what is 1/2+1/4+1/8

$\begin{array}{|rcll|} \hline && \frac12 + \frac14 + \frac18 \\ &=& \frac12 + \frac{1}{2^2} + \frac{1}{2^3} \\ &=& \frac12 \cdot ( 1 + \frac{1}{2} + \frac{1}{2^2} ) \\ &=& \frac12 \cdot [ 1 + \frac{1}{2} \cdot ( 1+ \frac{1}{2} ) ] \\ &=& \frac12 \cdot ( 1 + \frac{1}{2} \cdot \frac{3}{2} ) \\ &=& \frac12 \cdot ( 1 + \frac{3}{4} ) \\ &=& \frac12 \cdot \frac{7}{4} \\ &=& \frac{7}{8} \\ \hline \end{array}$