Question

Calculați E= pentru n €Z

Answer 1

Răspuns:

Explicație pas cu pas:

(9^n - 9^n-1)^1/2 = [9^(n-1) * (9 - 1)]^1/2 = [3^2(n-1) * 8]^1/2 = 3^(n-1)*8^1/2

[27^(n-1) - 19*27^(n-2)]^1/3 = [27^(n-2)(27 - 19)]^1/3 = [3^3(n-2) * 8]^1/3 =

= 3^(n-2)*8^1/3

3^(n-1)*8^1/2 / 3^(n-2)*8^1/3 = 8^(1/2 - 1/3) * 3^(n - 1 - n + 2) = 8^1/6 * 3 = 2^3/6 *3 = 2^1/2 * 3 = 3√2

(1/2 - 1/3 = 3/6 - 2/6 = 1/6)