\[\boxed{\text{994\ (994).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[b_{6} = \frac{1}{2},\ \ q = \frac{1}{2},\ \ S_{6} = ?\]
\[b_{6} = b_{1} \cdot q^{5},\]
\[b_{1} = \frac{b_{6}}{q^{5}} = \frac{1}{2} \cdot 2^{5} = 16.\]
\[S_{6} = b_{1} \cdot \frac{q^{6} - 1}{q - 1} = 16 \cdot \frac{\frac{1}{2^{6}} - 1}{\frac{1}{2} - 1\ } =\]
\[= 16 \cdot \left( - \frac{63}{64} \right) \cdot ( - 2) = \frac{63}{2} = 31,5.\]