Factorials
5! = 5 _ 4 _ 3 _ 2 _ 1
0! = 1
Canceling Out Factorials
Bigger factorial overshoots the smaller one by some numbers and that is the remaining factors.
8!/10! = 8!/(8! * 9 * 10) = 1/(10*9)
Simplifying
n!/(n+2)! = 1/[(n+1)(n+2)]
5! = 5 _ 4 _ 3 _ 2 _ 1
0! = 1
Bigger factorial overshoots the smaller one by some numbers and that is the remaining factors.
8!/10! = 8!/(8! * 9 * 10) = 1/(10*9)
n!/(n+2)! = 1/[(n+1)(n+2)]