Further closed forms for finite sums of weighted products of generalized fibonacci numbers

Melham, RS

Further 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, 2018, 56 (1), pp. 3 - 9
Issue Date:: 2018-02-01

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Field	Value	Language
dc.contributor.author	Melham, RS	en_US
dc.date.issued	2018-02-01	en_US
dc.identifier.citation	Fibonacci Quarterly, 2018, 56 (1), pp. 3 - 9	en_US
dc.identifier.issn	0015-0517	en_US
dc.identifier.uri	http://hdl.handle.net/10453/133376
dc.description.abstract	© 2018 Fibonacci Association. All rights reserved. The finite sum n 2−iFi−1 = 1 −Fn+2 2n , i=1 occurs in Section 9.1 of Knott [1], and is the inspiration for the present paper. We refer to the term 2−i in the summand as the weight term. Here, we present seven families of such finite sums that we believe to be new. In each of these seven families, the product that defines the summand can be made arbitrarily long. The sequences that we employ are generalizations of the Fibonacci/Lucas sequences.	en_US
dc.relation.ispartof	Fibonacci Quarterly	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Further closed forms for finite sums of weighted products of generalized fibonacci numbers	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	56	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	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	56	en_US

Abstract:

© 2018 Fibonacci Association. All rights reserved. The finite sum n 2−iFi−1 = 1 −Fn+2 2n , i=1 occurs in Section 9.1 of Knott [1], and is the inspiration for the present paper. We refer to the term 2−i in the summand as the weight term. Here, we present seven families of such finite sums that we believe to be new. In each of these seven families, the product that defines the summand can be made arbitrarily long. The sequences that we employ are generalizations of the Fibonacci/Lucas sequences.

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http://hdl.handle.net/10453/133376