Sociedad Colombiana de Matemáticas:Publicaciones
Lecturas Matemáticas
Volumen 25 [1] (2004)Páginas 15 - 24
Artículos Matemáticos

Fórmula de recorrência para a soma de séries infinitas

Jo\~ao Luiz Martins,Adilson J.V. Brand\~ao
Universidade Federal de Ouro Preto

Abstract. 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 $x$.

Palabras claves. Horadam's generalized numbers, Fibonacci sums, Pell sums.

Codigo AMS. 1991. Primary 11B37, 11B39.

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