Question

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

Answer 1

(n - 1)! + n! + (n + 1)! = (n + 1)²(n - 1)!
(n - 1)! + n(n - 1)! + n(n + 1)(n - 1)! = (n + 1)²(n - 1)!
(n - 1)!(1 + n + n( n + 1)) = (n² + 2n + 1)(n - 1)!
n² + 2n + 1 = n² + 2n + 1

Исходное равенство верно.