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1993•Glasgow Mathematical JournalOpen access

An identity for the Fibonacci and Lucas numbers

Derek Jennings

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Abstract

In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following identify.

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In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following identify.

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Available abstract

In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following identify.

Key concepts: Fibonacci number, Lucas number, Mathematics, Pisano period, Recurrence relation, Lucas sequence, Identity (music), Fibonacci polynomials

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