Fridy, J. A.; Roberts, Ian T. On sums of Fibonacci-type series. (English) Zbl 0685.10006 Aust. Math. Soc. Gaz. 16, No. 5, 130-132 (1989). 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 Cited in 1 Review MSC: 11B37 Recurrences 40A05 Convergence and divergence of series and sequences Keywords:convergence; power series with Fibonacci-type coefficients; series; of Fibonacci-type terms; rational expression PDFBibTeX XMLCite \textit{J. A. Fridy} and \textit{I. T. Roberts}, Aust. Math. Soc. Gaz. 16, No. 5, 130--132 (1989; Zbl 0685.10006)