Let Fn be the Fibonacci numbers, given by F1 = 1, F2 = 1, and for all integers n > 1, Fn+2 = Fn+1+ F„. Prove that for all integers n > 1, 2n E Fk-1 FR = F,F2 + F2F3 + ·… · + F2n-2F2n-1 + F2n-1F2n = F. k=2

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