Respostas

  • Usuário do Brainly
2014-08-21T22:22:23-03:00
A) \dfrac{6!}{3!}

Observe que, 6!=6\times5\times4\times3!, então:

\dfrac{6!}{3!}=\dfrac{6\times5\times4\times3!}{3!}=6\times5\times4=120

b) \dfrac{5!\cdot8!}{4!\cdot7!}

Note que, 8!=8\times7! e 5!=5\times4!.

Assim, \dfrac{5!\cdot8!}{4!\cdot7!}=\dfrac{5\times8\times4!\times7!}{4!\cdot7!}=5\times8=40

c) \dfrac{n!}{(n-1)!}

Observe que, n!=n(n-1)!.

Deste modo, \dfrac{n!}{(n-1)!}=\dfrac{n(n-1)!}{(n-1)!}=n.

d) \dfrac{n!}{(n+2)!}

Temos que, (n+2)!=(n+2)(n+1)n!.

Logo, \dfrac{n!}{(n+2)!}=\dfrac{n!}{(n+2)(n+1)n!}=\dfrac{1}{(n+2)(n+1)}.
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