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Fibonacci Sequence

Problem

Given the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, ... defined by the second order recurrence relation, Fn+2 = Fn + Fn+1. Prove that the nth term, Fn, is given by:

Fn = 
1
radical5
1 + radical5
2
n minus 
1 minus radical5
2
n
Problem ID: 135 (Nov 2003)     Difficulty: 4 Star

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