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

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  • Younseok Choo

    (Department of Electronic and Electrical Convergence Engineering, Hongik University, Sejong-Ro 2639, Sejong 30016, Korea)

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 , ⋯ .

Suggested Citation

  • Younseok Choo, 2021. "On the Reciprocal Sums of Products of Two Generalized Bi-Periodic Fibonacci Numbers," Mathematics, MDPI, vol. 9(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:178-:d:481965
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    References listed on IDEAS

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    1. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
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