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Topic: Fibonacci proof...help in understanding
Replies: 3   Last Post: Jan 23, 2008 1:00 AM

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Ladnor Geissinger

Posts: 313
From: University of North Carolina at Chapel Hill
Registered: 12/4/04
Re: Fibonacci proof...help in understanding
Posted: Jan 23, 2008 12:37 AM
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I think you will find this result much more transparent if you just write F(0)=0, F(1)=1, F(2)=1, F(3)=2, F(4)=3, etc for the Fibonacci number sequence.
Then note that 1+F(1)=F(3), so if we add F(2) to both expressions we will get 1+F(1)+F(2)=F(3)+F(2)=F(4), and then if we add F(3) to both expressions we will get
1+F(1)+F(2)+F(3)=F(4)+F(3)=F(5), etc. (i.e. by induction) it always works.

Note that I began with F(0)=0, the usual convention. But if you start with F(0)=1 as do a few textbook authors, then F(2)=2 and F(3)=3 so that in that case we would have at the beginning 2+F(1)=F(3), etc.



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