Fibonacci properties by matrix methods

Abstract

The Fibonacci sequence 0, 1, 1, 2, 3, 5, 8, 13, … is defined by u 0 = 0, u 1 = 1, and u n = u n −1 + u n −2 for . There are many elementary formulae relating the various u n , most of which, since the sequence is defined inductively, are themselves usually proved by induction.