Easy to see if you substitute in numbers.
Let n = 2 , then :
(n+2)! = 4! = 4 x 3 x 2 x 1
(n+1)! = 3! = 3 x 2 x 1
As you can see, when dividing, the 3 x 2 x 1 will cancel out only leaving 4 on top, which is n+2.
Therefore (n+2)! / (n+1)! = n+2
+250 
