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
Full paper (PDF, 167 Kb)

Details

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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