Question

if (n+1)!=12(n-1)! find the value of n

Answer 1

(n+1)!=(n+1)*n*(n-1)!
so the equation becomes
n*(n-1)=12
n^2-n=12
solving the above quadratic equation we will get the value of n

Answer 2

(n+1)! = 12(n-1)!
As we know, n! = n*(n-1)*(n-2)!
(n+1)! can be written as (n+1)*(n)*(n-1)!
Therefore,
{(n+1)*(n)*(n-1)!}/(n-1)! = 12
(n+1)*(n) = 12                 [because(n-1)! gets cancelled out.]
since 12 can be written as 4*3,
(n+1)*n = 4*3
on comparing both sides,
n+1 = 4 ; n=3
n=3