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

Publisher:
State University of West Georgia
Publication Type:
Journal Article
Citation:
Integers, 2012, 12
Issue Date:
2012-01
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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 Shars sum. Furthermore, we give an analogue for the Lucas numbers. Finally we note that our generalization of Shars sum and its analogue for the Lucas numbers carry over to certain one parameter generalizations of the Fibonacci and Lucas numbers.
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