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

Hančl, Jaroslav

Acta Arith. 59, No. 2, 97-104 (1991).

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