Question

FATORIAL

$a) \frac{12!}{10!+9!}$
$b) \frac{n!}{(n-2)!}$
$c) \frac{(n-1)!}{(n+2)!}$

Answer 1

Oi Daniel,

a)
$\frac{12!}{10!+9!} = \frac{12*11*10*9!}{9!(10+1)} = \frac{12*11*10}{11}= 12*10=\boxed{120}$

b)
$\frac{n!}{(n-2)!} = \frac{n*(n-1)*(n-2)!}{(n-2)!} = n*(n-1) = \boxed{n^2-n}$

c)
$\frac{(n-1)!}{(n+2)*(n+1)*n*(n-1)!} = \frac{1}{(n+2)*(n+1)*n} = \frac{1}{n^3+3n^2+2n} = \boxed{\frac{1}{n(n^2+3n+2)} }$

Bons estudos!