Open Access Open Access  Restricted Access Subscription or Fee Access

Infinite Family of Generalized Golden Ratios

Mohammed Yahdi

Abstract


The paper explores the generalization of the Fibonacci Golden Ratio to an infinite sequence of k-Golden Ratios. An extension of Binet’s Formula generates an infinite family of Fibonacci-like sequences. Each of these sequences is shown to possess the property that the quotient of consecutive terms converges to the corresponding k-Golden Ratio.

Keywords


Fibonacci sequence, Generalized Golden Ratio, Binet’s Formula

Full Text:

PDF


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.