A Proof of a Generic Fibonacci Identity From Wolfram’s MathWorld

Abstract

The generic identity involving the Fibonacci numbers, where C denotes the binomial coefficient counting the number of choices of elements from a set of k elements, is attributed on Wolfram’s MathWorld website to a personal communication from Aleksandrs Mihailovs. In spite of a very thorough search, we have been unable to find a published proof. We present here a combinatorial proof of our own, using the methods of Benjamin, Eustis and Plott.