Series of Floor and Ceiling Function—Part I: Partial Summations

Dhairya Shah, Manoj Sahni, Ritu Sahni, Ernesto León-Castro and Maricruz Olazabal-Lugo
Additional contact information
Dhairya Shah: School of Liberal Studies, Pandit Deendayal Energy University, Gandhinagar 382426, India
Manoj Sahni: Department of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar 382426, India
Ritu Sahni: School of Liberal Studies, Pandit Deendayal Energy University, Gandhinagar 382426, India
Ernesto León-Castro: Faculty of Economics and Administrative Sciences, Universidad Católica de la Santísima Concepción, Concepción 4090541, Chile
Maricruz Olazabal-Lugo: Department of Economics and Administrative, Universidad Autónoma de Occidente, Culiacan 80139, Mexico

Mathematics, 2022, vol. 10, issue 7, 1-19

Abstract: In this paper, we develop two new theorems relating to the series of floor and ceiling functions. We then use these two theorems to develop more than forty distinct novel results. Furthermore, we provide specific cases for the theorems and corollaries which show that our results constitute a generalisation of the currently available results such as the summation of first n Fibonacci numbers and Pascal’s identity. Finally, we provide three miscellaneous examples to showcase the vast scope of our developed theorems.

Keywords: ceiling function; floor function; Faulhaber’s formula; Fibonacci numbers; geometric series; partial summations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/7/1178/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/7/1178/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:7:p:1178-:d:786979

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().