Упр.24.2 ГДЗ Мордкович 10-11 класс (Алгебра)

а) yn = (-1)^n;
б) yn = (-2)^n / (n2 + 1);
в) yn = (-1)^n * 1/10^n;
г) yn = ((-1)^n + 2) / (3n — 2).

1. $$y_n = (-1)^n$$

   $$y_1 = (-1)^1 = -1$$
   
   $$y_2 = (-1)^2 = 1$$
   
   $$y_3 = (-1)^3 = -1$$
   
   $$y_4 = (-1)^4 = 1$$
   
   $$y_5 = (-1)^5 = -1$$

   $$-1;\ 1;\ -1;\ 1;\ -1$$

2. $$y_n = \frac{(-2)^n}{n^2+1}$$

   $$y_1 = \frac{(-2)^1}{1^2+1} = \frac{-2}{2} = -1$$
   
   $$y_2 = \frac{(-2)^2}{2^2+1} = \frac{4}{5}$$
   
   $$y_3 = \frac{(-2)^3}{3^2+1} = \frac{-8}{10} = -\frac{4}{5}$$
   
   $$y_4 = \frac{(-2)^4}{4^2+1} = \frac{16}{17}$$
   
   $$y_5 = \frac{(-2)^5}{5^2+1} = \frac{-32}{26} = -\frac{16}{13}$$

   $$-1;\ \frac{4}{5};\ -\frac{4}{5};\ \frac{16}{17};\ -\frac{16}{13}$$

3. $$y_n = (-1)^n \cdot \frac{1}{10^n}$$

   $$y_1 = (-1)^1 \cdot \frac{1}{10^1} = -\frac{1}{10}$$
   
   $$y_2 = (-1)^2 \cdot \frac{1}{10^2} = \frac{1}{100}$$
   
   $$y_3 = (-1)^3 \cdot \frac{1}{10^3} = -\frac{1}{1000}$$
   
   $$y_4 = (-1)^4 \cdot \frac{1}{10^4} = \frac{1}{10000}$$
   
   $$y_5 = (-1)^5 \cdot \frac{1}{10^5} = -\frac{1}{100000}$$

   $$-\frac{1}{10};\ \frac{1}{100};\ -\frac{1}{1000};\ \frac{1}{10000};\ -\frac{1}{100000}$$

4. $$y_n = \frac{(-1)^n+2}{3n-2}$$

   $$y_1 = \frac{(-1)^1+2}{3\cdot 1-2} = \frac{-1+2}{1} = 1$$
   
   $$y_2 = \frac{(-1)^2+2}{3\cdot 2-2} = \frac{1+2}{4} = \frac{3}{4}$$
   
   $$y_3 = \frac{(-1)^3+2}{3\cdot 3-2} = \frac{-1+2}{7} = \frac{1}{7}$$
   
   $$y_4 = \frac{(-1)^4+2}{3\cdot 4-2} = \frac{1+2}{10} = \frac{3}{10}$$
   
   $$y_5 = \frac{(-1)^5+2}{3\cdot 5-2} = \frac{-1+2}{13} = \frac{1}{13}$$

   $$1;\ \frac{3}{4};\ \frac{1}{7};\ \frac{3}{10};\ \frac{1}{13}$$

Ответ

а) $$-1;\ 1;\ -1;\ 1;\ -1$$
б) $$-1;\ \frac{4}{5};\ -\frac{4}{5};\ \frac{16}{17};\ -\frac{16}{13}$$
в) $$-\frac{1}{10};\ \frac{1}{100};\ -\frac{1}{1000};\ \frac{1}{10000};\ -\frac{1}{100000}$$
г) $$1;\ \frac{3}{4};\ \frac{1}{7};\ \frac{3}{10};\ \frac{1}{13}$$