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The Fibonacci series can be defined recursively as: F1 = 0; F2 = 1; and Fn...

The Fibonacci series can be defined recursively as: F1 = 0; F2 = 1; and Fn = Fn-2 + Fn-1. Show inductively that: (F1)2 + (F2)2 + ... + (Fn)2 = (Fn)(Fn+1).

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