Question

Найдите первые десять членов последовательности

$x_{n} = frac{(-1)^{n-1} }{10} <span> </span> [tex]c_{n} = 3^{(-1)n}$

Answer 1

1)   $x_{1} = frac{(-1)^{1-1} }{10} = frac{(-1)^{0} }{10} = frac{1 }{10} \ x_{2} = frac{(-1)^{2-1} }{10} = frac{(-1)^{1} }{10} = -frac{1 }{10} \ x_{3} = frac{(-1)^{3-1} }{10} = frac{(-1)^{2} }{10} = frac{1 }{10} \ x_{4} = frac{(-1)^{4-1} }{10} = frac{(-1)^{3} }{10} = -frac{1 }{10} ...$
$x_{1} = x_{3} =x_{3} =x_{3} =x_{3} = frac{1}{10} \ x_{2} = x_{4} =x_{6} =x_{8} =x_{10} = -frac{1}{10}$

2)   $c_{1} = 3^{(-1)*1} = 3^{(-1)} = frac{1}{3} \ c_{2} = 3^{(-1)*2} = 3^{1} = 3 \ c_{3} = 3^{(-1)*3} = 3^{(-1)} = frac{1}{3} \ c_{4} = 3^{(-1)*4} = 3^{1} = 3 \ c_{1} = c_{3} = c_{5} = c_{7} = c_{9} = frac{1}{3}\ c_{2} = c_{4} = c_{6} = c_{8} = c_{10} = 3$