Question

como resolver An,3=8.an,2​

Answer 1

Resposta:

$n=10$

Explicação passo a passo:

Note que:

$A_{n,3}= \frac{n!}{(n-3)!}\\\\A_{n,2}= \frac{n!}{(n-2)!}$

Substituindo na equação dada, teremos:

$A_{n,3}=8\cdot A_{n,2}\\\\\frac{n!}{(n-3)!}=8\cdot \frac{n!}{(n-2)!}\\\\\frac{n\cdot(n-1)\cdot(n-2)\cdot(n-3)!}{(n-3)!}=8\cdot \frac{n\cdot(n-1)\cdot(n-2)!}{(n-2)!}\\\\n\cdot(n-1)\cdot(n-2) = 8 \cdot n\cdot(n-1)\\\\\text{multiplique ambos lados por }\frac{1}{n\cdot(n-1)}:\\\\n-2=8\\\\n=10$