Question

Selesaikanlah soal di bawah ini :
1. (n+1)! = 5n!
2. (n+2)! = 20n!
3. n+1 C4 = n-1 C2

Answer 1

1)  (n + 1)! = 5.N!
 (n + 1)(n)(n - 1)(n- 2) ..... = 5 .n (n - 1)(n - 2)  ......  ----> bagi dengan n(n - 1)(n - 2) ..
n + 1 = 4
       n = 4 - 1
       n = 3
2) (n + 2) ! = 20 n!
    (n + 2)(n + 1) (n)(n - 1) ..= 20.n (n - 1) .... ------> bagi dengan n(n - 1)(n - 2) ....
    (n + 2)(n + 1) = 20
    n² + 3n + 2 = 20
    n² + 3n + 2 - 20 = 0
    n² + 3n - 18 = 0
   (n - 3)(n + 6) = 0
   n - 3 = 0  atau  x + 6 = 0
        n = 3 atau  x = - 6 (tak memenuhi)
3) ( n + 1) C 4 = (n - 1) C2
  = 
  = 
= 
= (n - 1)!
(n + 1)! = 12.(n - 1)!
(n + 1)(n)(n - 1)! = 12.(n - 1)!
(n + 1) n = 12
n² + n = 12
n² + n - 12 = 0
(n - 3)(n + 4) = 0
n - 3 = 0  atau n + 4 = 0
     n = 3  atau n = - 4 (tak memenuhi)

Answer 2

1. (n + 1)! = 5n!
(n + 1) n! / n! = 5
n + 1 = 5
n = 4

2. (n + 2) ! = 20 n!
(n + 2) (n + 1) n! = 20 n!
(n + 2) (n +1) = 20
n² + 3n + 2 = 20
n² + 3n - 18 = 0
(n + 6) (n -3) = 0
n = - 6  atau n = 3
ambil yang positif
n = 3

3. n+1 C4 = n -1 C2
(n + 1) ! / (n +1 - 4)! 4 ! = (n - 1)! / (n - 1 - 2)! 2!
(n + 1 )! / (n - 3)! 4 ! = (n - 1)! / (n - 3) ! 2!
(n + 1)! / 4! = (n - 1)! / 2!
(n + 1) n (n - 1)! / 24 = (n - 1)! / 2
(n + 1) n = 24/2
n² + n = 12
n² + n - 12 = 0
(n + 4) (n -3)
n = -4  atau n = 3
ambil yang positif
n =3