Sums of products of generalized Fibonacci and Lucas numbers
Hacene Belbachir (USTHB), Farid Bencherif (USTHB)
TL;DR
This paper derives new formulas for sums and alternating sums involving products of generalized Fibonacci and Lucas numbers, extending previous results with more straightforward methods.
Contribution
It introduces generalized formulas for sums of Fibonacci and Lucas products, simplifying and extending prior research in the field.
Findings
New formulas for sums of generalized Fibonacci and Lucas products
Extended previous results with more accessible proofs
Unified approach to sums and alternating sums
Abstract
In this paper, we establish several formulae for sums and alternating sums of products of generalized Fibonacci and Lucas numbers. In particular, we recover and extend all results of Z. Cerin and Z. Cerin & G. M. Gianella, more easily.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Combinatorial Mathematics · Advanced Mathematical Identities