Notes on a general sequence

Reza Farhadian; Rafael Jakimczuk

Published: 2020-05-08

Vol. 34 No. 2 (2020)

Notes on a general sequence

Reza Farhadian

, Rafael Jakimczuk

Abstract

Let {r_n}_n∈ℕ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula r_n ~ αβⁿ, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e. We also establish some asymptotic formulae and limits for the counting function of this sequence. All of the results are applied to some well-known sequences in mathematics.

Keywords:

general sequence , asymptotic formulae , limit behavior , the number e

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Farhadian, R., & Jakimczuk, R. (2020). Notes on a general sequence. Annales Mathematicae Silesianae, 34(2), 193–202. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/13611

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Reza Farhadian

farhadian.reza@yahoo.com
https://orcid.org/0000-0003-4027-9838

Affiliation:

Department of Statistics, Lorestan University, Iran Iran, Islamic Republic of

Rafael Jakimczuk

Affiliation:

División Matemática, Universidad Nacional de Luján, República Argentina Argentina

Vol. 34 No. 2 (2020)
Published: 2020-09-01

ISSN: 0860-2107

eISSN: 2391-4238

10.1515/amsil

Publisher

University of Silesia Press

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