A curious property of series involving terms of generalized sequences
Here we are concerned with series involving generalized Fibonacci numbers Un (p,q) and generalized Lucas numbers Vn (p,q). The aim of this paper is to find triples (p,q,r) for which the series Un (p,q)/rn and Vn (p,q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of t...
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200001873 |
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| _version_ | 1832554457119850496 |
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| author | Odoardo Brugia Piero Filipponi |
| author_facet | Odoardo Brugia Piero Filipponi |
| author_sort | Odoardo Brugia |
| collection | DOAJ |
| description | Here we are concerned with series involving generalized Fibonacci
numbers Un (p,q) and generalized Lucas numbers Vn (p,q). The aim of this paper is to find triples (p,q,r) for which the series Un (p,q)/rn and Vn (p,q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the
factor n. The results established in this paper generalize the
known fact that the series Fn/2n (Fn the nth Fibonacci number) and the series nFn/2n give the same result, namely −2/5. |
| format | Article |
| id | doaj-art-cf56e006ef104d49ab088e66716ebbc9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cf56e006ef104d49ab088e66716ebbc92025-02-03T05:51:29ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01231556310.1155/S0161171200001873A curious property of series involving terms of generalized sequencesOdoardo Brugia0Piero Filipponi1Fondazione Ugo Bordoni, Via B. Castiglione 59, Roma I-00142, ItalyFondazione Ugo Bordoni, Via B. Castiglione 59, Roma I-00142, ItalyHere we are concerned with series involving generalized Fibonacci numbers Un (p,q) and generalized Lucas numbers Vn (p,q). The aim of this paper is to find triples (p,q,r) for which the series Un (p,q)/rn and Vn (p,q)/rn (for r running from 0 to infinity) are unconcerned at the introduction of the factor n. The results established in this paper generalize the known fact that the series Fn/2n (Fn the nth Fibonacci number) and the series nFn/2n give the same result, namely −2/5.http://dx.doi.org/10.1155/S0161171200001873Generalized Fibonacci numberspower series. |
| spellingShingle | Odoardo Brugia Piero Filipponi A curious property of series involving terms of generalized sequences International Journal of Mathematics and Mathematical Sciences Generalized Fibonacci numbers power series. |
| title | A curious property of series involving terms of generalized sequences |
| title_full | A curious property of series involving terms of generalized sequences |
| title_fullStr | A curious property of series involving terms of generalized sequences |
| title_full_unstemmed | A curious property of series involving terms of generalized sequences |
| title_short | A curious property of series involving terms of generalized sequences |
| title_sort | curious property of series involving terms of generalized sequences |
| topic | Generalized Fibonacci numbers power series. |
| url | http://dx.doi.org/10.1155/S0161171200001873 |
| work_keys_str_mv | AT odoardobrugia acuriouspropertyofseriesinvolvingtermsofgeneralizedsequences AT pierofilipponi acuriouspropertyofseriesinvolvingtermsofgeneralizedsequences AT odoardobrugia curiouspropertyofseriesinvolvingtermsofgeneralizedsequences AT pierofilipponi curiouspropertyofseriesinvolvingtermsofgeneralizedsequences |