Решебник по алгебре и начала математического анализа 11 класс Колягин Проверь себя V

\[\mathbf{1.\ }\]

\[1)\ P_{7} = 7! = 7 \bullet 6 \bullet 5 \bullet 4 \bullet 3 \bullet 2 =\]

\[= 5040;\]

\[2)\ A_{8}^{3} = \frac{8!}{5!} = \frac{8 \bullet 7 \bullet 6 \bullet 5!}{5!} = 336;\]

\[3)\ C_{8}^{3} = \frac{8!}{3! \bullet 5!} = \frac{8 \bullet 7 \bullet 6 \bullet 5!}{3 \bullet 2 \bullet 5!} = 56;\]

\[4)\ \frac{P_{6}}{A_{7}^{5}} = 6! \bullet \frac{2!}{7!} = \frac{6! \bullet 2}{7 \bullet 6!} = \frac{2}{7}.\]

\[\mathbf{2}\text{.\ }\]

\[1)\ \frac{(n + 1)!}{(n - 1)!} = \frac{(n + 1)n(n - 1)!}{(n - 1)!} =\]

\[= n^{2} + n;\]

\[2)\ \frac{(n - 4)!}{(n - 2)!} =\]

\[= \frac{(n - 4)!}{(n - 2)(n - 3)(n - 4)!} =\]

\[= \frac{1}{n^{2} - 5n + 6}.\]

\[\mathbf{3}\text{.\ }\]

\[N = C_{9}^{3} = \frac{9!}{3! \bullet 6!} = \frac{9 \bullet 8 \bullet 7 \bullet 6!}{3 \bullet 2 \bullet 6!} =\]

\[= 3 \bullet 4 \bullet 7 = 84.\]

\[Ответ:\ \ 84.\]

\[\mathbf{4}.\]

\[N = A_{10}^{4} = \frac{10!}{6!} =\]

\[= \frac{10 \bullet 9 \bullet 8 \bullet 7 \bullet 6!}{6!} = 5040.\]

\[Ответ:\ \ 5040.\]

\[\mathbf{5}\text{.\ }\]

\[N = P_{6} = 6! =\]

\[= 6 \bullet 5 \bullet 4 \bullet 3 \bullet 2 \bullet 1 = 720.\]

\[Ответ:\ \ 720.\]

\[\mathbf{6}\text{.\ }\]

\[N = A_{10}^{3} = \frac{10!}{7!} =\]

\[= \frac{10 \bullet 9 \bullet 8 \bullet 7!}{7!} = 720.\]

\[Ответ:\ \ 720.\]

\[\mathbf{7}.\]

\[1)\ (x + y)^{6} =\]

\[2)\ (1 - a)^{5} =\]

\[= 1 - 5a + 10a^{2} - 10a^{3} + 5a^{4} - a^{5}.\]