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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)
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
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
Linking options:
https://www.mathnet.ru/eng/cheb1317 https://www.mathnet.ru/eng/cheb/v24/i2/p248
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Abstract page: | 58 | Full-text PDF : | 33 | References: | 6 |
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