On an expansion numbers on Fibonacci’s sequences
https://doi.org/10.22405/2226-8383-2023-24-2-248-255
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
$$𝑒 −Σ︁𝑛𝑘=0 1/𝑘!=(𝑥_𝑛)/𝑛!,1/(𝑛 + 1)≤ 𝑥𝑛 <1/𝑛.$$
Expressions of numbers over the sequence of inverse of Fibonacci numbers essentially uses these representation throw powers of “the gold section” 𝜙 = (1+√5)/2 .
About the Authors
Azar Giyasi
Allameh Tabataba’i University
Islamic Republic of Iran
Islamic Republic of Iran
candidate of physical and mathematical sciences
Ilya Petrovich Mikhailov
Kazan Aviation Institute
Russian Federation
Russian Federation
Vladimir Nikolaevich Chubarikov
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
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Review
For citations:
Giyasi A., Mikhailov I.P., Chubarikov V.N. On an expansion numbers on Fibonacci’s sequences. Chebyshevskii Sbornik. 2023;24(2):248-255. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-2-248-255
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