Question

calcule:
a)5!-4!

b)3.0!

c) 5!
_______
3!+2!

d) 105!
_______
104!

e)(2!)²×(6-1)!

f) 9!
______
7!-6!​

Answer 1

 Seja n um número natural, ou seja, inteiro e maior ou igual a 0, o fatorial de n será:

$n!=n\cdot(n-1)\cdot(n-2)\cdot...\cdot3\cdot 2\cdot 1$

 Ou seja, vamos multiplicando n por todos os seus antecessores naturais até o 1, e lembrando que $0!=1$.

-x-

a)

$5\cdot 4\cdot 3 \cdot 2 \cdot 1-4\cdot 3 \cdot 2\cdot 1\\20\cdot 6-12\cdot 2\\120-24\\96$

b)

$3\cdot0!\\3\cdot1\\3$

c)

$\dfrac{5!}{3!+2!}\\\\\dfrac{5\cdot 4\cdot 3\cdot 2\cdot 1}{3\cdot 2\cdot 1 +2\cdot1}\\\\\dfrac{120}{6+2}\\\\\dfrac{120}{8}\\\\15$

d)

$\dfrac{105!}{104!}\\\\\\\dfrac{105\cdot104!}{104!}\\\\105$

e)

$(2!)^2\cdot(6-1)!\\2^2\cdot5!\\4\cdot120\\480$

f)

$\dfrac{9!}{7!-6!}\\\\\dfrac{9\cdot 8\cdot 7\cdot 6!}{7\cdot6!-6!}\\\\\dfrac{72\cdot7\cdot6!}{6!\cdot(7-1)}\\\\\dfrac{72\cdot7}{6}\\\\12\cdot7\\\\84$

Dúvidas só perguntar!