Question

Simplifique a fração:

$\frac{(n+1)!}{(n+2)!}$

Answer 1

$n!=n\cdot(n-1)\cdot(n-2)\cdot(n-3)\cdot...\cdot3\cdot2\cdot1\\n!=n\cdot(n-1)!=n\cdot(n-1)\cdot(n-2)!=...$
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$\dfrac{(n+1)!}{(n+2)!}=\dfrac{(n+1)!}{(n+2)(n+1)!}\\\\\\\boxed{\boxed{\dfrac{(n+1)!}{(n+2)!}=\dfrac{1}{n+2}}}$