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Education > Math Undergrad > Re: induction w...
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Re: induction why is this wrong?

by chan <chalong08@[EMAIL PROTECTED] > May 1, 2008 at 12:41 PM

> if you want to show that F(n) < G(n), why don't you put it in?
> Assuming you have the same F(n) and G(n), then take G(n)-F(n)=3D
> \sum_1^n (2k) -\sum_1^n(2k-1)=3D\sum_1^n(2k-(2k-1)=3D\sum_1^n(1)=3Dn>0,
th=
us
> result. Or is F(n)(G(n)) the product from 1 to n of 2k-1 (2k)?

F(n) the product of the first n odd positive integers
G(n) the product of the first n even positive integers

Thus I plug in and did this:
4.Inductive proof that F(n)<G(n),	 n=991
P(n): F(n)<G(n)
P(1): F(1)<G(1)=3D(2*1-1)<(2*1)
=3D1<2 True
Assume P(n), that F(n)<G(n) Prove for P(n+1)
Proof:	F(n+1)=3DF(n)*(2n+1)
=3D(2n-1)(2n+1)
=3D 4n^2- 4n-1<G(n)(2n+2)
=3D 4n^2- 4n-1<(2n)(2n+2)
=3D4n^2- 4n-1<4n^2+2n

Do you think that this is valid?
 




 14 Posts in Topic:
induction why is this wrong?
chalong <chalong08@[EM  2008-04-30 23:34:43 
Re: induction why is this wrong?
se16@[EMAIL PROTECTED]   2008-05-01 04:18:09 
Re: induction why is this wrong?
chan <chalong08@[EMAIL  2008-05-01 11:55:22 
Re: induction why is this wrong?
Ansgar Wenzel <tdnpf@[  2008-05-01 20:13:50 
Re: How to work mathematical induction ?
Lasonia <ljkm2006@[EMA  2008-05-06 13:03:28 
Re: How to work mathematical induction ?
"[Mr.] Lynn Kurtz&qu  2008-05-06 17:40:12 
Re: How to work mathematical induction ?
Paul Sperry <plsperry@  2008-05-06 17:47:20 
Re: How to work mathematical induction ?
"Brian M. Scott"  2008-05-06 13:54:46 
Re: induction why is this wrong?
chan <chalong08@[EMAIL  2008-05-01 12:12:07 
Re: induction why is this wrong?
chan <chalong08@[EMAIL  2008-05-01 12:41:28 
Re: induction why is this wrong?
Ansgar Wenzel <tdnpf@[  2008-05-01 21:27:46 
Re: induction why is this wrong?
Paul Sperry <plsperry@  2008-05-01 21:24:14 
Re: induction why is this wrong?
chan <chalong08@[EMAIL  2008-05-01 14:28:59 
Re: induction why is this wrong?
Paul Sperry <plsperry@  2008-05-02 00:32:35 

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tan12V112 Sat Nov 22 17:19:04 CST 2008.