Our first purpose of this paper is to generalize Ostrowski's theorem to 1-generalized Fibonacci sequences. Furthermore, under certain conditions, we show that such a sequence splits into subsequences in general, and in this case, the asymptotic behavior of the sequence is periodically exponential-like. Also, we give a new proof of an explicit formula for a limiting value related with finitely generalized Fibonacci sequences.
All Science Journal Classification (ASJC) codes
- Applied Mathematics