Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 426

\[k \in N\ и\ k > 5.\]

\[1)\ 7! \bullet 8 = 8!\]

\[2)\ 16 \bullet 15! = 16!\]

\[3)\ 12! \bullet 13 \bullet 14 = 14!\]

\[4)\ k! \bullet (k + 1) = (k + 1)!\]

\[5)\ (k - 1)! \bullet k = k!\]

\[6)\ (k - 1)! \bullet k(k + 1) = (k + 1)!\]

\[7)\ (k - 2)! \bullet (k - 1)k = k!\]

\[8)\ (k - 5)! \bullet \left( k^{2} - 7k + 12 \right) =\]

\[= (k - 3)!\]

\[k^{2} - 7k + 12 = 0\]

\[D = 49 - 48 = 1\]

\[k_{1} = \frac{7 - 1}{2} = 3;\ \]

\[k_{2} = \frac{7 + 1}{2} = 4.\]