Jacobsthal-Lucas series and their applications

Abstract

In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence. In particular, we consider the properties of the set of incomplete sums as well as their applications. We prove that the set of incomplete sums of this series is a nowhere dense set of positive Lebesgue measure. Also we study singular random variables of Cantor type related to Jacobsthal-Lucas sequence.