On reciprocal series of generalized Fibonacci numbers with subscripts in arithmetic progression (Q764587)
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scientific article; zbMATH DE number 6014538
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On reciprocal series of generalized Fibonacci numbers with subscripts in arithmetic progression |
scientific article; zbMATH DE number 6014538 |
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On reciprocal series of generalized Fibonacci numbers with subscripts in arithmetic progression (English)
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13 March 2012
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Summary: We investigate formulas for closely related series of the forms: \[ \sum^\infty_{n=0} 1/(U_{an+b} + c),\quad \sum^\infty_{n=0} (-1)^n U_{an+b}/(U_{an+b} + c)^2, \quad \sum^\infty_{n=0} U_{2(an+b)}/(U^2_{an+b} + c)^2 \] for certain values of \(a, b\), and \(c\).
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