If (n + 1)! = 12 × [(n – 1)!], find the value of n.

To Find: Value of n


Given: (n+1)! = 12× [(n-1)!]


Formula Used: n! = (n) × (n-1) × (n-2) × (n-3) ………. 3 × 2 × 1


Now, (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 or, n = -4


But, n=-4 is not possible because in case of factorial (!) n can not be negative.


Hence, n=3 is the correct answer.


1