# the center of distances for some multigeometric series

## TL;DR

This paper studies the properties of the center of distances in sets related to multigeometric series, providing new conditions and complete descriptions for specific series types.

## Contribution

It introduces a new sufficient condition for the center of distances to be limited to 0 and the series terms, and offers a complete description for certain multigeometric series.

## Key findings

- Center of distances for achievement sets computed
- New condition for center of distances to be {0, series terms}
- Complete description for specific multigeometric series

## Abstract

Basic properties of the center of distances of a set are investigated. Computation of the center for achievement sets is particularly aimed at. A new sufficient condition for the center of distances of the set of subsums of a fast convergent series to consist of only 0 and the terms of the series is found. A complete description of the center of distances for some particular type of multigeometric series is provided. In particular, the center of distances $C(E)$ is the union of all centers of distances of $C(F_n)$ where $F_n$ is the set of all $n$-initial subsums of the discussed multigeometric series satisfying some special requirements. Several open questions are raised.