Question

Resolvendo a equação n!/(n-1)!=4 o valor de (n!-n) é igual:

a)20
b)24
c)28
d)32
e)36

Answer 1

$\frac{n!}{(n-1)!}=4\\\\\frac{n(n-1)!}{(n-1)!}=4\\\\\frac{n\cdot1}{1}=4\\\\\boxed{n=4}$
 
 Com efeito,

$(n!-n)=(4!-4)\\(n!-n)=4\cdot3\cdot2\cdot1-4\\(n!-n)=24-4\\\boxed{\boxed{(n!-n)=20}}$
 
 Opção "a"!!