On the transcendence of some infinite sums

Pingzhi Yuan, Juan Li

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 simp…