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.