They aren't equal. Take .
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hi,
I'm trying to do a proof by induction showing that (2x+1)!/(2^x (x)!) = ((2x+1)(2x-1)!)/(2^(x-1) (x-1)!) , but i don't quite remember factorial manipulation. I can recall that (x+1)! = (x+1)x! , but i can't remember if there's anything like this for (x-1)! or in this case, (2x-1)! as well.
any help is appreciated!
crap....
the proposition is:
1*3*5*...*(2x-1) = (2x-1)!/(2^(x-1) (x-1)!)
so i took the inductive step to (where x->x+1) :
1*3*5*...*(2x-1)*(2x+1) = (2x-1)!/(2^(x-1) (x-1)!) * (2x+1)
so i'm trying to get (2x-1)!/(2^(x-1) (x-1)!) * (2x+1) to equal
(2(x+1)-1)!/(2^((x+1)-1) ((x+1)-1)!) which equals (2x+1)!/(2^x (x)!), right?
or am i way off here?