Страница 208 номер 695, ГДЗ по алгебре за 9 класс к учебнику Мерзляка
Найдите второй, седьмой и сотый члены последовательности \((b_n)\), заданной формулой \(n\)-го члена: 1) \(b_n = \frac{10}{n}\); 2) \(b_n = 5 - 2n\); 3) \(b_n = n^2 + 2n\); 4) \(b_n = (-1)^{n+1}\).
1) \(b_{n} = \frac{10}{n}\)
\(b_{2} = \dfrac{10}{2} = 5;\ b_{7} = \dfrac{10}{7};\ b_{100} = \dfrac{10}{100} = 0{,}1\)
2) \(b_{n} = 5 - 2n\)
\(b_{2} = 5 - 2 \cdot 2 = 1\)
\(b_{7} = 5 - 2 \cdot 7 = 5 - 14 = - 9\)
\(b_{100} = 5 - 2 \cdot 100 = 5 - 200 = - 195\)
3) \(b_{n} = n^{2} + 2n\)
\(b_{2} = 2^{2} + 2 \cdot 2 = 4 + 4 = 8\)
\(b_{7} = 7^{2} + 2 \cdot 7 = 49 + 14 = 63\)
\(b_{100} = 100^{2} + 2 \cdot 100 = 10000 + 200 = 10200\)
4) \(b_{n} = ( - 1)^{n + 1}\)
\(b_{2} = ( - 1)^{2 + 1} = ( - 1)^{3} = - 1\)
\(b_{7} = ( - 1)^{7 + 1} = ( - 1)^{8} = 1\)
\(b_{100} = ( - 1)^{100 + 1} = ( - 1)^{101} = - 1\)
Ответ: 1) \(b_{2} = 5;\ b_{7} = \frac{10}{7};\ b_{100} = 0{,}1\); 2) \(b_{2} = 1;\ b_{7} = - 9;\ b_{100} = - 195\); 3) \(b_{2} = 8;\ b_{7} = 63;\ b_{100} = 10200\); 4) \(b_{2} = - 1;\ b_{7} = 1;\ b_{100} = - 1\).
