Transcendence of some infinite series

Fedoua Sghiouer, Kacem Belhroukia, Ali Kacha

Published 2023-01-16Version 1

In the present paper and as an application of Roth's theorem concerning the rational approximation of algebraic numbers, we give a sufficient condition that will assure us that a series of positive rational terms is a transcendental number. With the same conditions, we establish a transcendental measure of $ \sum_{n = 1}^{\infty} 1/a_n$.