\[\boxed{\text{713\ (713).}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[\textbf{а)}\ b_{1} = 1,\ \ b_{2} = x,\]
\[q = \frac{b_{2}}{b_{1}} = x,\ \ n = 5,\]
\[S_{5} = b_{1} \cdot \frac{q^{5} - 1}{q - 1} = \frac{x^{5} - 1}{x - 1}.\]
\[\textbf{б)}\ b_{1} = 1,\ \ b_{2} = - x,\]
\[q = \frac{b_{2}}{b_{1}} = - x,\ \ n = 7,\]
\[S = b_{1} \cdot \frac{q^{7} - 1}{q - 1} = \frac{- x^{7} - 1}{- x - 1} =\]
\[= \frac{x^{7} + 1}{x + 1}.\]