Re: understanding induction problems
- From: "Paul E. Black" <p.black@xxxxxxx>
- Date: Thu, 01 May 2008 13:00:53 -0400
On Thursday 01 May 2008 02:09, chalong wrote:
Suppose that I am to prove by Inductive proof that F(n)G(n)=(2n)!, n?1
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) = (2n-1)(2n)=(2n)! for n?1
P(1) = (2*1-1)(2*1)=(2*1)!
(1)(2)=(2*1)!
2=2 TRUE
Let's try P(2) just for support.
P(2) = (2*2-1)(2*2) =? (2*2)!
(4-1)(4) =? 4!
3*4 /= 4*3*2*1
So the formula doesn't even work for P(2).
Assume P(n) Prove P(n+1)
Trying to prove a falsehood is always hard.
I think you mean
F(n) = PROD_(1 to n) (2k-1) = 1 * 3 * ... * 2n-1
and
G(n) = PROD_(1 to n) (2k) = 2 * 4 * ... * 2n
-paul-
.
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- From: chalong
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