Question

Boa Noite galera alguem poderia me ajudar a resolver esse exercício de fatorial?
a) n! sobre (n-2)! e
b) (n+1)! sobre (n+2)!
grato e irei aguardar pois estou se matando rsrsrs...

Answer 1

$\boxed{\boxed{x!=x\cdot(x-1)\cdot(x-2)\cdot(x-3)\cdot...\cdot3\cdot2\cdot1}}\\\\\\\boxed{\boxed{x!=x\cdot(x-1)!=x\cdot(x-1)\cdot(x-2)!=...}}$
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a)

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

b)

$\dfrac{(n+1)!}{(n+2)!}=\dfrac{(n+1)!}{(n+2)!(n+2-1)!}\\\\\\\dfrac{(n+1)!}{(n+2)!}=\dfrac{(n+1)!}{(n+2)\cdot(n+1)!}\\\\\\\boxed{\boxed{\dfrac{(n+1)!}{(n+2)!}=\dfrac{1}{n+2}}}$