Two Calculation Methods of the Sum of Reciprocals of All Products Generated by Prime Factors of the Number 2022

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60162694%3AG43__%2F24%3A00560611" target="_blank" >RIV/60162694:G43__/24:00560611 - isvavai.cz</a>

Výsledek na webu

<a href="https://mitav.unob.cz/data/Mitav2023.pdf" target="_blank" >https://mitav.unob.cz/data/Mitav2023.pdf</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Two Calculation Methods of the Sum of Reciprocals of All Products Generated by Prime Factors of the Number 2022

Popis výsledku v původním jazyce

This paper is inspired by one task on the sum of a special infinite series on the Berkeley Math Circle. The task was to determine the sum of all the unit fractions that have denominators with only factors consisting of all prime divisors of the number 2002, i.e. the primes 2, 7, 11, 13. We updated this task to determine the sum of reciprocals of all products generated by all prime divisors of the number 2022. This series can be consider as the reduced harmonic series generated by three primes 2, 3, 337. The sum of this series was calculated analytically by two methods and also numerically by using the programming language of the computer algebra system Maple 2022. By these three attempts we obtained the same result. Finally, we generalized the obtained result and presented a formula for the sum of these series with n generating positive integers different from 1.

Název v anglickém jazyce

Two Calculation Methods of the Sum of Reciprocals of All Products Generated by Prime Factors of the Number 2022

Popis výsledku anglicky

This paper is inspired by one task on the sum of a special infinite series on the Berkeley Math Circle. The task was to determine the sum of all the unit fractions that have denominators with only factors consisting of all prime divisors of the number 2002, i.e. the primes 2, 7, 11, 13. We updated this task to determine the sum of reciprocals of all products generated by all prime divisors of the number 2022. This series can be consider as the reduced harmonic series generated by three primes 2, 3, 337. The sum of this series was calculated analytically by two methods and also numerically by using the programming language of the computer algebra system Maple 2022. By these three attempts we obtained the same result. Finally, we generalized the obtained result and presented a formula for the sum of these series with n generating positive integers different from 1.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

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Návaznosti

V - Vyzkumna aktivita podporovana z jinych verejnych zdroju

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

MITAV 2023

ISBN

978-80-7582-290-1

ISSN

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e-ISSN

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Počet stran výsledku

10

Strana od-do

60-69

Název nakladatele

Fakulta elektrotechniky a komunikačních technologií Vysokého učení technického v Brně

Místo vydání

Brno

Místo konání akce

Brno

Datum konání akce

15. 6. 2023

Typ akce podle státní příslušnosti

EUR - Evropská akce

Kód UT WoS článku

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