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Three Series for the Generalized Golden Mean
- Publication Year :
- 2014
- Publisher :
- arXiv, 2014.
-
Abstract
- As is well-known, the ratio of adjacent Fibonacci numbers tends to phi = (1 + sqrt(5))/2, and the ratio of adjacent Tribonacci numbers (where each term is the sum of the three preceding numbers) tends to the real root eta of X^3 - X^2 - X - 1 = 0. Letting alpha(n) denote the corresponding ratio for the generalized Fibonacci numbers, where each term is the sum of the n preceding, we obtain rapidly converging series for alpha(n), 1/alpha(n), and 1/(2-alpha(n)).
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4541af4e46f609fd5a4cbdcce158b71b
- Full Text :
- https://doi.org/10.48550/arxiv.1401.6200