<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>{rn}n</italic>∈𝕅 be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula <italic>rn ~ αβn</italic>, where <italic>α, β</italic> are real numbers with <italic>α ></italic> 0 and <italic>β ></italic> 1. In this note we prove some limits that connect this sequence to the number <italic>e</italic>. 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.</abstract>

Let {rn}n∈𝕅 be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ 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.

Notes on a General Sequence

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Notes on a General Sequence"}

Let {rn}n∈𝕅 be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0...

Notes on a General Sequence

Data publikacji: 08 maj 2020

Zakres stron: 193 - 202

Otrzymano: 28 sty 2020

Przyjęty: 18 kwi 2020

DOI: https://doi.org/10.2478/amsil-2020-0006

Słowa kluczowe
general sequence, asymptotic formulae, limit behavior, the number

© 2020 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Notes on a General Sequence

Data publikacji: 08 maj 2020

Zakres stron: 193 - 202

Otrzymano: 28 sty 2020

Przyjęty: 18 kwi 2020

DOI: https://doi.org/10.2478/amsil-2020-0006

Słowa kluczowegeneral sequence, asymptotic formulae, limit behavior, the number

© 2020 Reza Farhadian et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Słowa kluczowe
general sequence, asymptotic formulae, limit behavior, the number