In this paper we investigate the infinite convergent sum $T=\sum_{ n=0}^\infty\frac{ P(n)}{ Q(n)}$, where $P(x)\in\bar{ \mathbb{ Q}}[x]$, $Q(x)\in\mathbb{ Q}[x]$ and $Q(x)$ has only simple rational zeros. N. Saradha and R. Tijdeman have obtained sufficient and necessary conditions for the transcendence of $T$ if the degree of $Q(x)$ is 3. In this paper we give sufficient and necessary conditions for the transcendence of $T$ if the degree of $Q(x)$ is 4 and $Q(x)$ is reduced.
Categories: math.NT