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Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers


Affiliations
1 Department of Mathematics, National Institute of Technology, Rourkela, India
     

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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.

Keywords

Balancing Numbers, Lucas-balancing Numbers, Telescoping Summation Formula.
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  • Adegoke, K., Factored closed-form expressions for the sums of cubes of Fibonacci and Lucas numbers, https://arxiv.org/pdf/1706.08469.pdf.
  • Adegoke, K., Sums of fourth powers of Fibonacci and Lucas numbers, https://arxiv.org/pdf/1706.00407.pdf.
  • Behera, A., Panda, G.K., On the square roots of triangular numbers, Fib. Quart., 37(2)(1999), 98–105.
  • Clary, S., Hemenway, P.D., On sums of cubes of Fibonacci numbers, in Applications of Fibonacci Numbers, Kluwer Academic Publishers, Dordrecht, The Netherlands, 5 (1993), 123–136.
  • 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.

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  • Sum Formulas Involving Powers of Balancing and Lucas-balancing Numbers

Abstract Views: 45  |  PDF Views: 0

Authors

S. G. Rayaguru
Department of Mathematics, National Institute of Technology, Rourkela, India
G. K. Panda
Department of Mathematics, National Institute of Technology, Rourkela, India

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.

Keywords


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

References