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On sums of Fibonacci-type series. (English) Zbl 0685.10006

Let \(\{a_ n\}^{\infty}_{n=1}\) be a sequence of real numbers defined by \(a_ n=c_ 1a_{n-1}+c_ 2a_{n-2}+...+c_ ma_{n-m}\) \((n>m)\), where \(a_ 1,...,a_ m\) and \(c_ 1,...,c_ m\) are given constants with \(c_ 1+...+c_ m\neq 1\). The main result of the paper shows that if the series \(\sum^{\infty}_{n=1}a_ n\) is convergent, then its sum can be given by a rational expression of the constants \(c_ i's\) and \(a_ i's\) \((i=1,2,...,m)\).
Reviewer: P.Kiss

MSC:

11B37 Recurrences
40A05 Convergence and divergence of series and sequences
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