Найдите сумму бесконечной геометрической прогрессии -40; 20; -10…

\[- 40;20;\ - 10;\ldots\]

\[b_{1} = - 40;\ \ b_{2} = 20;\ \]

\[q = \frac{b_{2}}{b_{1}} = \frac{20}{- 40} = - \frac{1}{2};\]

\[S = \frac{b_{1}}{1 - q} = \frac{- 40}{1 + \frac{1}{2}} = - 40\ :\frac{3}{2} =\]

\[= - 40 \cdot \frac{2}{3} = - \frac{80}{3} = - 26\frac{2}{3}.\]

\[Ответ:\ - 26\frac{2}{3}.\]