## Abstract

Convergent sums $T=∑n=1∞P(n)/Q(n)$ and $U=∑n=1∞(-1)nP(n)/Q(n)$, where P(X), Q(X) ∈ Q[X], and Q(X) has only simple rational roots, are investigated. Adhikari, Shorey and the authors have shown that T and U are either rational or transcendental. Simple necessary and sufficient conditions are formulated for the transcendence of T and U if the degree of Q is 3 and 2, respectively.