Analogues of a Fibonacci-Lucas Identity
Gaurav Bhatnagar
TL;DR
This paper presents a new telescoping proof and generalizations of a Fibonacci-Lucas identity, extending the results to other sequences with similar recurrence relations.
Contribution
It introduces an alternative proof method and generalizes the identities to broader classes of sequences satisfying three-term recurrences.
Findings
Provided a telescoping proof of the Fibonacci-Lucas identity
Generalized identities to other recurrence-based sequences
Extended the scope of Fibonacci-Lucas identities to new sequences
Abstract
Sury's 2014 proof of an identity for Fibonacci and Lucas numbers (Identity 236 of Benjamin and Quinn's 2003 book: {\em Proofs that count: The art of combinatorial proof}) has excited a lot of comment. We give an alternate, telescoping, proof of this---and associated---identities and generalize them. We also give analogous identities for other sequences that satisfy a three-term recurrence relation.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematics and Applications · Advanced Combinatorial Mathematics