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


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.

