Some Notes of Iteration Double Sequences and Double Series on Real Number

DOI

10.2991/978-94-6463-332-0_6How to use a DOI?

Keywords

Convergent; Double Sequences; Double Series; Iterated Series

Abstract

A development of single sequences and single series (with domain N ) is double sequences and double series (with domain N × N ). The discussion in this research focuses specifically on the iterated series of a double series. The research method used is literature review. The study begins by providing a definition of an iterated series, then shows its properties related to the convergence of double series. This research concludes that if a double series converges to s ∈ R then the following applies: (1) Iterated series ∑ n = 1 ∞ ∑ m = 1 ∞ x n , m = s if and only if ∑ m = 1 ∞ x n , m exists for every n ∈ N , (2) Iterated series ∑ m = 1 ∞ ∑ n = 1 ∞ x n , m = s if and only if ∑ n = 1 ∞ x n , m exists for every m ∈ N . On the other hand, a double series where the terms can be expressed as the product of two single series which converge respectively to x ∈ R and y ∈ R , then the double series converges to xy and both iterated series also have the value xy . All double sequences and double series discussed are limited to the codomain of real numbers.

Copyright

© 2023 The Author(s)

Open Access

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

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TY  - CONF
AU  - Sahlan Sidjara
AU  - Muhammad Abdy
AU  - Rahmat Syam
AU  - Muhammad Harun Nur Rasyid
AU  - Farhan Dakhil Shyaa
PY  - 2023
DA  - 2023/12/18
TI  - Some Notes of Iteration Double Sequences and Double Series on Real Number
BT  - Proceedings of the 5th International Conference on Statistics, Mathematics, Teaching, and Research 2023 (ICSMTR 2023)
PB  - Atlantis Press
SP  - 42
EP  - 53
SN  - 2352-538X
UR  - https://doi.org/10.2991/978-94-6463-332-0_6
DO  - 10.2991/978-94-6463-332-0_6
ID  - Sidjara2023
ER  -