Let's rewrite the left side of the equation:
(n-1)! + n! + (n+1)= n! + (n-1)! (1+n+n(n+1)= n! + (n-1)! (n+1) (n+1= n! + n! (n-1) (n+1= n! (1 + (n-1)(n+1)= n! (1 + (n^2 - 1)= n! (n^2= n! * n^2
Then, the left side of the equation becomes:
n! n^2 = (n+1)^2 (n-1)= (n+1)^2(n-1)!.
Therefore, the equation (n-1)! + n! + (n+1)! = (n+1)^2(n-1)! is proven to be true.
Let's rewrite the left side of the equation:
(n-1)! + n! + (n+1)
= n! + (n-1)! (1+n+n(n+1)
= n! + (n-1)! (n+1) (n+1
= n! + n! (n-1) (n+1
= n! (1 + (n-1)(n+1)
= n! (1 + (n^2 - 1)
= n! (n^2
= n! * n^2
Then, the left side of the equation becomes:
n! n^2 = (n+1)^2 (n-1)
= (n+1)^2(n-1)!.
Therefore, the equation (n-1)! + n! + (n+1)! = (n+1)^2(n-1)! is proven to be true.