Solve the equation n! + (n+1)! = (n+2)!.

n! + (n+1)! =
(n+2)!

Let us rewrite:

n!+ (n+1)n! =
(n+2)(n+1)n!

Factorize n!

n!(1+n+1) =
(n+2)(n+1)n!

Divide by n!

==> n+2 =
(n+2)(n+1)

No divide by (n+2)

==> 1= n+1

==> n = 0

to verify substitute with n=0

==>
0! + 1! = 2!

==> 1+1 = 2

==>
2=2