A family of Cantorvals

Abstract

The set of subsums of the series ∑n=1∞$\begin{array}{} \sum_{n=1}^{\infty} \end{array}$ xn is known to be one of three types: a finite union of intervals, homeomorphic to the Cantor set, or of the type known as a Cantorval. Bartoszewicz, Filipczak and Szymonik have described a family of series which contained all known examples of subsum sets which are Cantorvals. We construct another family of series which produces new examples of subsum sets which are Cantorvals.

Keywords

• subsum sets
• cantor set
• cantorval
• multigeometric series
• 40a05