Series of Floor and Ceiling Function—Part I: Partial Summations
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 general...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1178 |
| _version_ | 1797438454330556416 |
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| author | Dhairya Shah Manoj Sahni Ritu Sahni Ernesto León-Castro Maricruz Olazabal-Lugo |
| author_facet | Dhairya Shah Manoj Sahni Ritu Sahni Ernesto León-Castro Maricruz Olazabal-Lugo |
| author_sort | Dhairya Shah |
| collection | DOAJ |
| description | 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 <i>n</i> Fibonacci numbers and Pascal’s identity. Finally, we provide three miscellaneous examples to showcase the vast scope of our developed theorems. |
| first_indexed | 2024-03-09T11:38:08Z |
| format | Article |
| id | doaj.art-6f153b26aac84513a2f8cac741ad407e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:08Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6f153b26aac84513a2f8cac741ad407e2023-11-30T23:38:18ZengMDPI AGMathematics2227-73902022-04-01107117810.3390/math10071178Series of Floor and Ceiling Function—Part I: Partial SummationsDhairya Shah0Manoj Sahni1Ritu Sahni2Ernesto León-Castro3Maricruz Olazabal-Lugo4School of Liberal Studies, Pandit Deendayal Energy University, Gandhinagar 382426, IndiaDepartment of Mathematics, School of Technology, Pandit Deendayal Energy University, Gandhinagar 382426, IndiaSchool of Liberal Studies, Pandit Deendayal Energy University, Gandhinagar 382426, IndiaFaculty of Economics and Administrative Sciences, Universidad Católica de la Santísima Concepción, Concepción 4090541, ChileDepartment of Economics and Administrative, Universidad Autónoma de Occidente, Culiacan 80139, MexicoIn 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 <i>n</i> Fibonacci numbers and Pascal’s identity. Finally, we provide three miscellaneous examples to showcase the vast scope of our developed theorems.https://www.mdpi.com/2227-7390/10/7/1178ceiling functionfloor functionFaulhaber’s formulaFibonacci numbersgeometric seriespartial summations |
| spellingShingle | Dhairya Shah Manoj Sahni Ritu Sahni Ernesto León-Castro Maricruz Olazabal-Lugo Series of Floor and Ceiling Function—Part I: Partial Summations Mathematics ceiling function floor function Faulhaber’s formula Fibonacci numbers geometric series partial summations |
| title | Series of Floor and Ceiling Function—Part I: Partial Summations |
| title_full | Series of Floor and Ceiling Function—Part I: Partial Summations |
| title_fullStr | Series of Floor and Ceiling Function—Part I: Partial Summations |
| title_full_unstemmed | Series of Floor and Ceiling Function—Part I: Partial Summations |
| title_short | Series of Floor and Ceiling Function—Part I: Partial Summations |
| title_sort | series of floor and ceiling function part i partial summations |
| topic | ceiling function floor function Faulhaber’s formula Fibonacci numbers geometric series partial summations |
| url | https://www.mdpi.com/2227-7390/10/7/1178 |
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