Help

S = (1/2) ( 1 - (1/2)^6 )  / ( 1 - 1/2)    =  63/64     ( we could see this from the other problem )

This 6-term geometric series has first term $a_0 = \frac12$ and ratio 1/2, so it has value

$\begin{align*} \frac{\frac12(1-\left(\frac12\right)^{6})}{1-\frac12} &= 1-\left(\frac12\right)^{6}\\ &= 1-\frac1{64}\\ &= \boxed{\frac{63}{64}}. \end{align*}$