What is the value of 1×1!+2×2!+3×3!+............n×n!; where n! means n factorial or n(n-1)(n-2)...1

For natural number n, (n!)2>nn if

P(n):1.2+2.3+3.4+...+n(n+1)=(n+1)(n+2)3 The statement P(n) is