JimT wrote:
> Not elegant.
> Define F(n) as a Fibonacci sequence starting with 1, 1 etc.
> Define Proposition_n: Phi^n = F(n)*Phi + F(n-1)
> Phi^2 = 1*Phi + 1
> Therefore Proposition_2 is true
> Assume Proposition_n is true for all n st 2 \leq n \leq k
> So  Phi^k = F(k)*Phi + F(k-1)
> Phi^(k+1) = F(k)*Phi^2 + F(k-1)*Phi
>           = F(k)*Phi + F(k) + F(k-1)*Phi
>           = F(k+1)*Phi + F(k)
> So Proposition_(k+1) is true
> By induction Proposition_n is true for n \geq 2.
> 
Damn! I should have got that (((8(|) Doh!

> 3rd entry on Googling fibonacci sequence is:
> www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html
> 
Yup, seen that. Lots of good stuff there but I don't think he shows the 
proof above. iirc he only shows the definition.

John

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