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Chebyshevskii Sbornik, 2023, Volume 24, Issue 2, Pages 248–255
DOI: https://doi.org/10.22405/2226-8383-2023-24-2-248-255
(Mi cheb1317)
 

BRIEF MESSAGES

On an expansion numbers on Fibonacci's sequences

A. Kh. Ghiyasia, I. P. Mikhailovb, V. N. Chubarikovc

a Allameh Tabataba’i University (Iran)
b Kazan Aviation Institute (Leninogorsk)
c Lomonosov Moscow State University (Moscow)
References:
Abstract: In this paper theorems on the expression of real numbers on Fibonacci sequence. It pay a special attention to “explicit formulas” and conditions of the uniqueness of such representations. We note that unifiing of an expression of a real number over inverse values of a multiplicaticative system permits to get the estimation of the form
$$ e-\sum_{k=0}^n\frac 1{k!}=\frac{x_n}{n!}, \frac 1{n+1}\leq x_n<\frac 1n. $$
Expressions of numbers over the sequence of inverse of Fibonacci numbers essentially uses these representation throw powers of “the gold section” $\varphi=\frac{1+\sqrt 5}{2}.$
Keywords: the Fibonacci's sequence.
Received: 06.03.2023
Accepted: 14.06.2023
Document Type: Article
UDC: 511.3
Language: Russian
Citation: A. Kh. Ghiyasi, I. P. Mikhailov, V. N. Chubarikov, “On an expansion numbers on Fibonacci's sequences”, Chebyshevskii Sb., 24:2 (2023), 248–255
Citation in format AMSBIB
\Bibitem{GhiMikChu23}
\by A.~Kh.~Ghiyasi, I.~P.~Mikhailov, V.~N.~Chubarikov
\paper On an expansion numbers on Fibonacci's sequences
\jour Chebyshevskii Sb.
\yr 2023
\vol 24
\issue 2
\pages 248--255
\mathnet{http://mi.mathnet.ru/cheb1317}
\crossref{https://doi.org/10.22405/2226-8383-2023-24-2-248-255}
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