On the sums of Fibonacci and Lucas sequences or the art of cancelling $1−x$

descriptionPublicationkeyboard_double_arrow_right Article 12 Oct 2017Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Elemente der Mathematik, volume 72, pages 171-172 (issn: 0013-6018, eissn: 1420-8962,

Copyright policy )

Authors: Paunić, Đura;

doi: 10.4171/em/340

On the sums of Fibonacci and Lucas sequences or the art of cancelling $1−x$

- Summary
- Subjects
- Metrics

Abstract

The author establishes the identity \[ \sum_{k=0}^n m^kL-k + (m-2) \sum_{k=0}^{n+1} m^{k-1} F_k = m^{n+1} F_{n+1}, \] for nonnegatiev integer $n$ and real $m>0$, $F_n$, $L_n$ denote the Fibonacci numbers and Lucas numbers, thereby generalizing previous Fibonacci-Lucas relations of Sury and Marques.

Related Organizations

University of Novi Sad
Serbia

Keywords

Fibonacci and Lucas numbers and polynomials and generalizations

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

0

Average

gold