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

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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