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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |