Closed forms for finite sums of weighted products of generalized Fibonacci numbers

Melham, RS

Closed forms for finite sums of weighted products of generalized Fibonacci numbers

Melham, RS

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Publication Type:: Journal Article
Citation:: Fibonacci Quarterly, 2017, 55 (2), pp. 99 - 104
Issue Date:: 2017-05-01

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Field	Value	Language
dc.contributor.author	Melham, RS	en_US
dc.date.issued	2017-05-01	en_US
dc.identifier.citation	Fibonacci Quarterly, 2017, 55 (2), pp. 99 - 104	en_US
dc.identifier.issn	0015-0517	en_US
dc.identifier.uri	http://hdl.handle.net/10453/125925
dc.description.abstract	In this paper, we present closed forms for certain finite sums of weighted products of generalized Fibonacci numbers. Indeed, we present seven multi-parameter families of such finite sums, all of which we believe to be new. In each of these families, the number of factors in the summand is governed by the size of the integer parameter j ≥ 1, and can be made as large as we please. We present our main results in terms of sequences that generalize the Fibonacci/Lucas numbers. Consequently, each of our main results can be specialized to involve the Fibonacci/Lucas numbers. For instance, as a consequence of one of our main results, it follows that (Equation presented) Here the weight term in the summand is 2i-1.	en_US
dc.relation.ispartof	Fibonacci Quarterly	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Closed forms for finite sums of weighted products of generalized Fibonacci numbers	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	55	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
utslib.for	0199 Other Mathematical Sciences	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
utslib.copyright.status	open_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	55	en_US

Abstract:

In this paper, we present closed forms for certain finite sums of weighted products of generalized Fibonacci numbers. Indeed, we present seven multi-parameter families of such finite sums, all of which we believe to be new. In each of these families, the number of factors in the summand is governed by the size of the integer parameter j ≥ 1, and can be made as large as we please. We present our main results in terms of sequences that generalize the Fibonacci/Lucas numbers. Consequently, each of our main results can be specialized to involve the Fibonacci/Lucas numbers. For instance, as a consequence of one of our main results, it follows that (Equation presented) Here the weight term in the summand is 2i-1.

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http://hdl.handle.net/10453/125925