Thread: Factorials

I understand how to find them when numbers are involved. However, my problem is I can not figure out how to do it with n terms.

Example:



Any help will be greatly appreciated.

Originally Posted by mathgeek777

I understand how to find them when numbers are involved. However, my problem is I can not figure out how to do it with n terms.

Example:



Any help will be greatly appreciated.

Hint:

Hmm, try using the fact that n!= n(n-1)!=n(n-1)(n-2)!

Originally Posted by mathgeek777

I understand how to find them when numbers are involved. However, my problem is I can not figure out how to do it with n terms.

Example:



Any help will be greatly appreciated.

=

Do you see where you can cancel and reduce the expression?

i dont know how sound this logic is since i haven't done factorials in a long time but maybe it will steer you in some sort of direction


(2n)!
------
(2n-2)!

gives:

1x2x3...x(2n-3) x(2n-2) x (2n-1) x (2n)
--------------------------------------
1x2x3...x((2n-2)-1) x (2n-2)

this leaves (2n-1)(2n)

So the answer is 2n(2n-1)?

Originally Posted by mathgeek777

So the answer is 2n(2n-1)?

Yes!

try it out, test the values n = 3,4,5 first by inserting in the original expression and expanding and simplifying and then second by inserting the values n into 2n(2n-1) and you should get the same answer