A note on a family of alternating Fibonacci sums

Robert Frontczak
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 22, 2016, Number 2, Pages 64—71
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Authors and affiliations

Robert Frontczak
Landesbank Baden-Wuerttemberg
Am Hauptbahnhof 2, 70173 Stuttgart, Germany

Abstract

In this note we consider a family of finite and infinite alternating sums containing products of Fibonacci numbers. We derive closed-form expressions for this family of sums. As a consequence of this result we establish new algebraic relationships between certain alternating sums of reciprocals of products of Fibonacci numbers with integer power.

Keywords

  • Fibonacci number
  • Alternating sums
  • Reciprocals

AMS Classification

  • 11B37
  • 11B39

References

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  9. Melham, R.S. (2002) Reduction Formulas for the Summation of Reciprocals in Certain Second-Order Recurring Sequences, The Fibonacci Quarterly, 40(1), 71–75.
  10. Melham, R.S. (2003) On Some Reciprocal Sums of Brousseau: An Alternative Approach to that of Carlitz, The Fibonacci Quarterly, 41(1), 59–62.
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Cite this paper

APA

Frontczak, R. (2016). A note on a family of alternating Fibonacci sums. Notes on Number Theory and Discrete Mathematics, 22(2), 64-71.

Chicago

Frontczak, Robert. “A Note on a Family of Alternating Fibonacci Sums.” Notes on Number Theory and Discrete Mathematics 22, no. 2 (2016): 64-71.

MLA

Frontczak, Robert. “A Note on a Family of Alternating Fibonacci Sums.” Notes on Number Theory and Discrete Mathematics 22.2 (2016): 64-71. Print.

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