Question

Simplifique os fatoriais dos números abaixo (desenvolva os fatoriais - não coloque somente resposta): a)15!/12! = b)5!/3! = c)5!/(4 −1)! = d)0! 9!/7! = e)(n + 1)!/(n+1) n! = f)5! 20!/18! 1! 6! = g)5! . 3!/2! . 6!! = h)8!/4!. 3! = i)7! . 2!!/(7−2)! = j)12!/10!

Answer 1

Resposta Final: A) 2730, B) 20, C) 20, D) 72, E) 1, F) 190/3, G) 1/2, H) 280, I) 84, J) 132

a) 15!/12! = (15 . 14 . 13 . 12!)/12! = 15 . 14 . 13 = 2730

b) 5!/3! = (5 . 4 . 3!)/3! = 5 . 4 = 20

c) 5!/(4 - 1)! = 5!/3! = (5 . 4 . 3!)/3! = 5 . 4 = 20

d) (0! 9!)/7! = (1 . 9!)/7! = (9 . 8 . 7!)/7! = 9 . 8 = 72

e) (n + 1)!/(n + 1) n! = [(n + 1) . n!]/(n + 1) . n! = 1

f) (5! 20!)/(18! 1! 6!) = (5! . 20 . 19 . 18!)/(18! . 6 . 5!) = (20 . 19)/6 = 380/6 = 190/3

g) (5! 3!)/(2! 6!) = (5! . 3 . 2!)/(2! . 6 . 5!) = 3/6 = 1/2

h) 8!/(4! 3!) = (8 . 7 . 6 . 5 . 4!)/(4! 3!) = (8 . 7 . 6 . 5)/3! = 1680/6 = 280

i) (7! . 2!)/(7 - 2)! = (7! . 2!)/5! = (7 . 6 . 5! . 2!)/5! = 7 . 6 . 2 . 1 = 84

j) 12!/10! = (12 . 11 . 10!)/10! = 12 . 11 = 132