The Zeckendorf representation of a positive integer is the unique expression of this integer as the sum of distinct Fibonacci numbers, where no two of these Fibonacci numbers are consecutive terms in the Fibonacci sequence and where the term f1 = 1 is not used (but the term f2 = 1 may be used).
Define the generalized Fibonacci numbers recursively by g1= a, g2= b, and gn = gn_1+ gn−2 for n ≥ 3. Show that gn = afn−2+ bfn_1, for n ≥ 3.
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