# On expansions of numbers in alternating *s*-adic series and Ostrogradskii series of the first and second kind

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We present expansions of real numbers in alternating where τ

*s*-adic series (1 <*s*∈*N*), in particular,*s*-adic Ostrogradskii series of the first and second kind. We study the “geometry” of this representation of numbers and solve metric and probability problems, including the problem of structure and metric-topological and fractal properties of the distribution of the random variable$$ {\xi } = \frac{1}{s^{{\tau_1} - 1}} + \sum\limits_{k = 2}^\infty {\frac{{\left( { - 1} \right)}^{k - 1}}{s^{{\tau_1} + {\tau_2} + ... + {\tau_k} - 1}},} $$

_{ k }are independent random variables that take natural values.## Keywords

Fractal Property Independent Random Variable Absolute Continuity Irrational Number Infinite Product
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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