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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dhairya Shah & Manoj Sahni & Ritu Sahni & Ernesto León-Castro & Maricruz Olazabal-Lugo, 2022. "Series of Floor and Ceiling Function—Part I: Partial Summations," Mathematics, MDPI, vol. 10(7), pages 1-19, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1178-:d:786979
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    Cited by:

    1. Dhairya Shah & Manoj Sahni & Ritu Sahni & Ernesto León-Castro & Maricruz Olazabal-Lugo, 2022. "Series of Floor and Ceiling Functions—Part II: Infinite Series," Mathematics, MDPI, vol. 10(9), pages 1-17, May.

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