Fórmula de recorrencia para a soma de séries infinitas envolvendo sequencias do tipo Horadam.

• Autores: Joao Luiz Martins, Adison J.V. Brandao
• Localización: Lecturas matemáticas, ISSN-e 0120-1980, Vol. 25, Nº. 1, 2004, págs. 15-24
• Idioma: español
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• Resumen

  • In this article we introduce a recurrence formula for certain infinite series whose terms include factors that belong to a generalized Horadam-type sequence. This recurrence formula is used to calculate the $\displaystyle{\sum_{n=1}^{+\infty}n^{k}W_{n}x^{n}}$ series sum without use of derivatives and at a lower computation cost. Some results are presented below which were obtained by numerical implementation of the recurrence formula for some particular values of $k$ and $x$.