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 Post subject: Induction proofPosted: Mon, 20 Sep 2010 19:27:28 UTC
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Joined: Sat, 18 Sep 2010 21:28:18 UTC
Posts: 15
Given
(F_k)^2 = F_b F_{b+1} for b>=1

Prove by induction that if F_k is the kth Fibonacci number.

Base F(1)^2= F(1)*F(2)
1=1*1
1=1 True

Induction k=b

(F(k))^2=F(k)*F(k+1)

(F(k))^2=(F(k))^2+1

Last edited by mebigp on Wed, 22 Sep 2010 00:34:00 UTC, edited 9 times in total.

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 Post subject: Posted: Mon, 20 Sep 2010 19:31:04 UTC
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9633
Please correct any typos in the problem statement.

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 Post subject: Posted: Mon, 20 Sep 2010 21:30:35 UTC
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Joined: Sat, 18 Sep 2010 21:28:18 UTC
Posts: 15
The typos were corrected

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 Post subject: Posted: Mon, 20 Sep 2010 22:00:42 UTC
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Joined: Wed, 1 Oct 2003 04:45:43 UTC
Posts: 9633
No, not all of them were fixed...

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 Post subject: Posted: Tue, 21 Sep 2010 00:48:20 UTC
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Joined: Sat, 18 Sep 2010 21:28:18 UTC
Posts: 15
I think I corrected them all

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 Post subject: Re: Induction proofPosted: Tue, 21 Sep 2010 19:03:23 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6009
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
mebigp wrote:
Given
(F_k)^2 = F_b F_{b+1} for b>=1

Prove by induction that if F_k is the kth Fibonacci number.

How is k related to b?

mebigp wrote:
Base F(1)^2= F(1)*F(2)
1=1*1
1=1 True

Induction k=n

(F(k))^2=F(k)*F(k+1)

(F(k))^2=(F(k))^2+1

Huh? What exactly are you doing?

mebigp wrote:
The typos were corrected

Obviously not.

_________________

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 Post subject: Posted: Wed, 22 Sep 2010 00:35:55 UTC
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Joined: Sat, 18 Sep 2010 21:28:18 UTC
Posts: 15
Should of been let k=b

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 Post subject: Re: Induction proofPosted: Wed, 22 Sep 2010 16:05:35 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7951
Location: Lexington, MA
Hello, mebigp!

I don't see any corrections . . .

Quote:
Given
(F_b)^2 = F_b*F_{b+1} for b >= 1
. . First of all, this is not true!

"The square of F_b is the product of F_b and the next Fibonacci number" ?

. .
I don't think so!

Prove by induction that if F_k is the kth Fibonacci number.

Base: F(1)^2 = F(1)*F(2)
. . . . . . . . .1 = 1*1
. . . . . . . . .1 = 1 True

Induction k=b

(F_k)^2 = F_k*F_(k+1)

(F_k)^2 = (F_k)^2 + 1 . what?

A number = the number plus one ?

No one can reply . . . The problem is all wrong!

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 Post subject: Re: Induction proofPosted: Thu, 23 Sep 2010 16:05:39 UTC
 S.O.S. Oldtimer

Joined: Sun, 4 Nov 2007 12:08:30 UTC
Posts: 245
Location: Bratislava, Slovakia
Soroban wrote:
No one can reply . . . The problem is all wrong!

My guess is that the intended problem could be something like:
Given that , and , prove that is the n-th Fibonacci number.

(It's not that hard to do this by induction.)

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