Hitunglah nilai n dari persamaan berikut. a. (n + 4)! = 9(n + 3)! b. (n + 3)! = 20(n + 1)!

Faktorial:
n! = (n - 1)(n - 2)(n - 3)(n - 4)...

a.
(n + 4)! = 9(n + 3)!
(n + 4)(n + 4 - 1)! = 9(n + 3)!
(n + 4)(n + 3)! = 9(n + 3)!
(n + 4) = 9
n + 4 = 9
n = 9 - 4
n = 5

b.
(n + 3)! = 20(n + 1)!
(n + 3)(n + 3 - 1)(n + 3 - 2)! = 20(n + 1)!
(n + 3)(n + 2)(n + 1)! = 20(n + 1)!
(n + 3)(n + 2) = 20
n² + 3n + 2n + 6 = 20
n² + 5n + 6 - 20 = 0
n² + 5n - 14 = 0
n² + 7n - 2n - 14 = 0
n(n + 7) - 2(n + 7) = 0
(n + 7)(n - 2) = 0
n + 7 = 0     atau     n - 2 = 0
n = -7          atau     n = 2