Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 19

\[\boxed{\mathbf{19}\mathbf{.}}\]

\[1)\ 6;\ 1;\ \frac{1}{6};\ \ldots;\]

\[b_{1} = 6\ \ и\ \ b_{2} = 1;\]

\[q = \frac{b_{2}}{b_{1}} = \frac{1}{6};\]

\[S = \frac{b_{1}}{1 - q} = \frac{6}{1 - \frac{1}{6}} = 6\ :\frac{5}{6} =\]

\[= 6 \bullet \frac{6}{5} = \frac{36}{5} = 7,2;\]

\[Ответ:\ \ 7,2.\]

\[2)\ - 25;\ - 5;\ - 2;\ \ldots;\]

\[b_{1} = - 25\ \ и\ \ b_{2} = - 5;\]

\[q = \frac{b_{2}}{b_{1}} = \frac{- 5}{- 25} = \frac{5}{25} = \frac{1}{5};\]

\[S = \frac{b_{1}}{1 - q} = \frac{- 25}{1 - \frac{1}{5}} = - 25\ :\frac{4}{5} =\]

\[= - 25 \bullet \frac{5}{4} = - \frac{125}{4} = - 31,25;\]

\[Ответ:\ \ - 31,25.\]