Jacobsthal-Lucas series and their applications

In this paper we study the properties of positive series such that its terms are reciprocals of the elements of Jacobsthal-Lucas sequence ($J_{n+2}=2J_{n+1}+J_n$, $J_1=2$, $J_2=1$). 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.