Vol. 28, No. 3, 1969

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ISSN: 0030-8730
Representation of real numbers by generalized geometric series

Eugene A. Maier

Vol. 28 (1969), No. 3, 603–609
Abstract

We shall say that the series of real numbers, i=01∕ai, is a generalized geometric series (g.g.s.) if and only if ai2 ai+1ai1 for all i 1. (Note that the series is geometric if and only if equality holds.) In this paper we investigate the representation of positive real numbers less than or equal to one by generalized geometric series of the form i=0xi∕ci where the ci are positive integers and x 1.

Mathematical Subject Classification
Primary: 40.10
Secondary: 10.00
Milestones
Received: 20 March 1968
Published: 1 March 1969
Authors
Eugene A. Maier