Jamieson, M. J. Fibonacci numbers and Aitken sequences revisited. (English) Zbl 0735.11007 Am. Math. Mon. 97, No. 9, 829-831 (1990). G. M. Phillips [Am. Math. Mon. 91, 354-357 (1984; Zbl 0545.65004)] has shown that Aitken’s transformation applied to the sequence of ratios of consecutive Fibonacci numbers yields further ratios of Fibonacci numbers and that this remains true if the transformation is iterated. In the present note this is generalized to ratios of every p-th Fibonacci number. Reviewer: R.F.Tichy (Graz) Cited in 1 ReviewCited in 3 Documents MSC: 11B39 Fibonacci and Lucas numbers and polynomials and generalizations Keywords:Aitken’s transformation; ratios of Fibonacci numbers Citations:Zbl 0545.65004 PDFBibTeX XMLCite \textit{M. J. Jamieson}, Am. Math. Mon. 97, No. 9, 829--831 (1990; Zbl 0735.11007) Full Text: DOI