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Fibonacci numbers and Aitken sequences revisited. (English) Zbl 0735.11007

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)

MSC:

11B39 Fibonacci and Lucas numbers and polynomials and generalizations

Citations:

Zbl 0545.65004
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