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On Finite Sums of Good and Shar that Involve Reciprocals of Fibonacci Numbers

Recently Nathaniel Shar presented a finite sum, involving the Fibonacci numbers, that generalizes a classical result first considered by I. J. Good and others. In this paper we provide a generalization of Shar’s sum. Furthermore, we give an analogue for the Lucas numbers. Finally we note that our generalization of Shar’s sum and its analogue for the Lucas numbers carry over to certain one parameter generalizations of the Fibonacci and Lucas numbers.