induction why is this wrong?

Suppose that I am to prove by Inductive proof that F(n)G(n)=3D(2n)!, n=991
and my F(n) is the (2k-1) from 1 to n and G(n) is 2k from 1 to n
How do i prove this? I try this so far by i got stuck please help.
P(n)  =3D  (2n-1)(2n)=3D(2n)!       for n=991
P(1)    =3D        (2*1-1)(2*1)=3D(2*1)!
(1)(2)=3D(2*1)!
2=3D2  TRUE

Assume P(n) Prove P(n+1)

Proof:  P(n+1)  =3D (2n-1)(2n)+(2(n+1)-1)*(2(n+1))=3D (2(n+1))!
=3D (2n)!+2n+2n+2 =3D (2n+2)!
=3D(2n)!+(4n+2)=3D(2n+2)!
I cannot get that left hand side to equal (2n+2)! anyway  i tried.
What is the correct way to do this?
Also maybe i shouldn't replace F(n) by 2n-1 and G(n) by 2k by leave
them in as part of proof?