Closed forms for certain fibonacci type sums that involve second order products

Melham, RS

Closed forms for certain fibonacci type sums that involve second order products

Melham, RS

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Publication Type:: Journal Article
Citation:: Fibonacci Quarterly, 2017, 55 (3), pp. 195 - 200
Issue Date:: 2017-08-01

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Field	Value	Language
dc.contributor.author	Melham, RS	en_US
dc.date.issued	2017-08-01	en_US
dc.identifier.citation	Fibonacci Quarterly, 2017, 55 (3), pp. 195 - 200	en_US
dc.identifier.issn	0015-0517	en_US
dc.identifier.uri	http://hdl.handle.net/10453/126061
dc.description.abstract	In this paper, we present closed forms for certain finite sums in which the summand is a product of generalized Fibonacci numbers. We present our results in the form of six theorems that feature a generalized Fibonacci sequence {Wn}, and an accompanying sequence {Wn}- We add a further layer of generalization to our results with the use of three parameters s, k, and m. The inspiration for this paper comes from a website of Knott that lists so-called order 2 summations involving the Fibonacci and Lucas numbers. Probably the most well-known of these summations is σni=1Fi2=FnFn+1.	en_US
dc.relation.ispartof	Fibonacci Quarterly	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Closed forms for certain fibonacci type sums that involve second order products	en_US
dc.type	Journal Article
utslib.citation.volume	3	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	3	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 in which the summand is a product of generalized Fibonacci numbers. We present our results in the form of six theorems that feature a generalized Fibonacci sequence {Wn}, and an accompanying sequence {Wn}- We add a further layer of generalization to our results with the use of three parameters s, k, and m. The inspiration for this paper comes from a website of Knott that lists so-called order 2 summations involving the Fibonacci and Lucas numbers. Probably the most well-known of these summations is σni=1Fi2=FnFn+1.

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http://hdl.handle.net/10453/126061