On the Reciprocal Sums of Products of Two Generalized Bi-Periodic Fibonacci Numbers

Younseok Choo
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Younseok Choo: Department of Electronic and Electrical Convergence Engineering, Hongik University, Sejong-Ro 2639, Sejong 30016, Korea

Mathematics, 2021, vol. 9, issue 2, 1-11

Abstract: This paper concerns the properties of the generalized bi-periodic Fibonacci numbers { G n } generated from the recurrence relation: G n = a G n − 1 + G n − 2 ( n is even) or G n = b G n − 1 + G n − 2 ( n is odd). We derive general identities for the reciprocal sums of products of two generalized bi-periodic Fibonacci numbers. More precisely, we obtain formulas for the integer parts of the numbers ∑ k = n ∞ ( a / b ) ξ ( k + 1 ) G k G k + m − 1 , m = 0 , 2 , 4 , ? , and ∑ k = n ∞ 1 G k G k + m − 1 , m = 1 , 3 , 5 , ? .

Keywords: bi-periodic Fibonacci numbers; reciprocal; floor function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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