Question

Resolva as equações.

Answer 1

Resposta:

a) 2

b) 6

c) 27

Explicação passo-a-passo:

a)

$\dfrac{(n+2)!}{n!} =12$

$\dfrac{(n+2)*(n+1)*n!}{n!} =12$

(n+2)*(n+1) = 12

n² + n + 2n + 2 = 12

n² + 3n - 10 = 0

n = -5  n = 2

Pela definição de fatorial n > 0, assim:

n = 2

b)

$\dfrac{(n-2)!}{(n-1)!} =\dfrac{1}{5}$

$\dfrac{(n-2)!}{(n-1)*(n-2)!} =\dfrac{1}{5}$

n - 1 = 5

n = 6

c)

$\dfrac{(n+1)! + n!}{(n+2)!} =\dfrac{1}{28}$

$\dfrac{(n+1)*n! + n!}{(n+2)*(n+1)*n!} =\dfrac{1}{28}$

$\dfrac{n!(n + 1 + 1)}{(n+2)*(n+1)*n!} =\dfrac{1}{28}$

$\dfrac{(n + 2)}{(n+2)*(n+1)} =\dfrac{1}{28}$

n + 1 = 28

n = 27