Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers

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Authors

  • S. G. Rayaguru
     ,IN
  • G. K. Panda
     ,IN

DOI:

https://doi.org/10.18311/jims/2019/21623

Keywords:

Balancing Numbers, Lucas-balancing Numbers, Telescoping Summation Formula.
11B39

Abstract

In this article, we obtain the closed form expressions for different types of summation formulas involving certain powers of balancing and Lucas-balancing numbers using the telescoping summation formula.

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Published

2018-12-12

How to Cite

Rayaguru, S. G., & Panda, G. K. (2018). Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers. The Journal of the Indian Mathematical Society, 86(1-2), 137–160. https://doi.org/10.18311/jims/2019/21623

Issue

Volume 86, Issue 1-2, January-June 2019

Section

Articles

License

Copyright (c) 2018 S. G. Rayaguru, G. K. Panda

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2018-07-21
Accepted 2023-01-30
Published 2018-12-12

 

References

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Davala, R.K., Panda, G.K., On Sum and Ratio Formulas for Balancing Numbers, Journal of the Ind. Math. Soc., 82(1–2) (2015).

Melham, R.S., Alternating sums of fourth powers of Fibonacci and Lucas numbers, Fib. Quart., 38(3) (2000), 254–259.

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