The Journal of the Indian Mathematical Society

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Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers


Affiliations
1 Department of Center for Data Science, Siksha ’O’ Anusandhan Deemed to be University, Bhubaneswar - 751 030, India
2 Department of Mathematics, National Institute of Technology, Rourkela - 769 008, India
     

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In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers.


Keywords

Balancing numbers, Lucas-balancing numbers, gap balancing numbers, t-balancing numbers.
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  • K. Adegoke, Generalizations of the Reciprocal Fibonacci-Lucas Sums of Brousseau, J. Integer Seq., Vol. 21 (2018), Article 18.1.6.

  • A. Behera and G. K. Panda, On the square roots of triangular numbers, Fibonacci Quart., 37(2) (1999), 98–105.

  • Bro. A. Brousseau, Summation of Infinite Fibonacci series, Fib. Quart., 7 (1969), 143–168.

  • Bro. A. Brousseau, Fibonacci-Lucas Infinite Series-Research Topic, Fib. Quart., 7 (1969), 211–217.

  • R. K. Davala and G. K. Panda, On Sum and Ratio Formulas for Balancing Numbers, J. Indian Math. Soc., 82(1-2) (2015), 23–32.

  • R. Frontczak, New results on reciprocal series related to Fibonacci and Lucas numbers with subscripts in arithmetic progression, Int. J. Contemporary Math. Sci., 11 (2016), 509–516.

  • G. K. Panda, Some fascinating properties of balancing numbers, In Proc. of Eleventh Internat. Conference on Fibonacci Numbers and Their Applications, Cong. Numerantium, 194 (2009), 185–189.

  • S. G. Rayaguru and G. K. Panda, Some infinite product identities involving balancing and Lucas-balancing numbers, Alabama J. Math., 42 (2018).

  • S. G. Rayaguru and G. K. Panda, Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers, J. Indian Math. Society, 86(1-2) (2019), 1–24.

  • S. G. Rayaguru and G. K. Panda, Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers-II, Notes on Number Theory and Discrete Mathematics, 25(3) (2019), 102–110.


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  • Brousseau’s Reciprocal Sums Involving Balancing and Lucas-Balancing Numbers

Abstract Views: 180  |  PDF Views: 0

Authors

S. G. Rayaguru
Department of Center for Data Science, Siksha ’O’ Anusandhan Deemed to be University, Bhubaneswar - 751 030, India
G. K. Panda
Department of Mathematics, National Institute of Technology, Rourkela - 769 008, India

Abstract


In this paper, we derive the closed form expressions for the finite and infinite sums with summands having products of balancing and Lucas-balancing numbers in the denominator. We present some generalized Brousseau’s sums for balancing and Lucas-balancing numbers.


Keywords


Balancing numbers, Lucas-balancing numbers, gap balancing numbers, t-balancing numbers.

References





DOI: https://doi.org/10.18311/jims%2F2022%2F22177