Hullo! This is my first time using this site. I have just begun tutoring a Math 12 student and I'm a little rusty on factorials. The stuff I'm stuck on is why : n!/(n-2)! = n(n-1).
I seem to be able to come up with the solutions to the following (solving for n) but I can't figure out what to do with the n! in questions like :
(1) (n+1)!/n! = 6 (I know the answer is n = 5 but don't know where the n! goes..)
(n+1)!/n! = 6
I know that n has to be one less than 6 because everything else is going to cancel out : 6x5x4x3x2x1/5x4x3x2x1 = 6
(2) (n+2!)/n! = 12
I know the answer is 2 because I got as far as : (n+2)! = 12 x n! (n+2)!/2 = 6 x n!
So I somehow got here by subtracting 2 from both sides but I think I'm missing a step : n!/2 = 4!/2 = 12
Then I'm stumped on :
(n+1)!/(n-2!) = 20 (n-1)
(n+1)! = 6 (n-1)! (I realised n = 2 here because on the left, 3! = 6 so n = 2 but I can't show the working..)
Any help would be appreciated...I know I must be missing just one fundamental thing somewhere...