(n+2)\n!-(3n+2)\(n+1)!=
= ((n+2)·(n + 1) - 3n - 2)/n+1)! =
= (n² + 3n + 2 - 3n - 2)/n+1)! =
= n²/(n+1)! =
(n+2)\n!-(3n+2)\(n+1)!=
= ((n+2)·(n + 1) - 3n - 2)/n+1)! =
= (n² + 3n + 2 - 3n - 2)/n+1)! =
= n²/(n+1)! =