## Expression of real numbers with the help of infinite series.(English)Zbl 0701.11005

The paper consists of three theorems which describe conditions for a set $$S$$ and for a sequence $$\{a_ n\}^{\infty}_{n=1}$$ in order that every real number $$B\in (0,\varepsilon]$$ should be expressible in the form $$B=\sum^{\infty}_{n=1}1/a_ n$$, where $$a_n\in S$$. A criterion for rationality of not too quickly increasing sequences is also presented as a consequence.
Reviewer: J.Hančl

### MSC:

 11J72 Irrationality; linear independence over a field 11B34 Representation functions

### Keywords:

representation of real numbers; rationality
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