Geodesic
On an expansion numbers on Fibonacci's sequences
Čebyševskij sbornik, Tome 24 (2023) no. 2, pp. 248-255

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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. 
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     author = {A. Kh. Ghiyasi and I. P. Mikhailov and V. N. Chubarikov},
     title = {On an expansion numbers on {Fibonacci's} sequences},
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A. Kh. Ghiyasi; I. P. Mikhailov; V. N. Chubarikov. On an expansion numbers on Fibonacci's sequences. Čebyševskij sbornik, Tome 24 (2023) no. 2, pp. 248-255. http://geodesic.mathdoc.fr/item/CHEB_2023_24_2_a12/