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factorials

I have 2n+12×(2n)!2n(n)!\frac{2n+1}{2}\times \frac{(2n)!}{2^n(n)!} and I am trying to show that it equals (2n+2)!2n+1(n+1)!\frac{(2n+2)!}{2^{n+1}(n+1)!} but I don't seem to be able to get it right.

I have multiplied the top and bottom by (n+1) but that doesn't seem to quite do it?
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BJack
19
Is this the whole question? I think what you have on the LHS is equal to (2n+2)!2n+2(n+1)!\frac{(2n+2)!}{2^{n+2}(n+1)!}, i.e. an additional factor of 1/2. :s-smilie:

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