Question

1a) 3!5!/4!6!
d) h!/(n - 2!
e) (n+1)!/(n+2)
f) (n+3)!/(n-2)! . (n-1)!/n+1)!

Answer 1

a) $\frac{3!5!}{4!6!}=\frac{3!5!}{4.3!.6.5!}=\frac{1}{24}$

d) $\frac{n!}{(n-2)!}=\frac{n.(n-1).(n-2)!}{(n-2)!}=n(n-1)$

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

f) ${\frac{(n+3)!}{(n-2)!}}.{\frac{(n-1)!}{(n+1)!}}=\\{\frac{(n+3)(n+2)(n+1)n(n-1)(n-2)!}{(n-2)!}}.{\frac{(n-1)!}{(n+1)n(n-1)!}}=\\{(n+3)(n+2)(n+1)n(n-1)}.{\frac{1}{(n+1)n}=\\(n+3)(n+2)(n-1)$

O Mozean espera ter ajudado!