The Fibonacci numbers Fn are defined by the conditions: F0=0, F1=1, and Fn+1 = Fn + Fn-1 for all n ≥ 1. Show that F2=1, F3=2, F4=3, and compute F5, F6 and F7.
Compute Fn+1Fn-1 − F02 for a few values of n; guess a general formula and prove it by induction, or otherwise.
By induction on k, or otherwise, show that Fn+k=FkFn+1+Fk-1Fn for all positive integers n and k.
A minimum of blind calculation 
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