# Irrationality Criteria for Series by Erdős and Straus

May 12, 2020

### Abstract

We formalise certain irrationality criteria for infinite series of the form: $\sum_{n=1}^\infty \frac{b_n}{\prod_{i=1}^n a_i}$ where $\{b_n\}$ is a sequence of integers and $\{a_n\}$ a sequence of positive integers with $a_n >1$ for all large n. The results are due to P. Erdős and E. G. Straus [1]. In particular, we formalise Theorem 2.1, Corollary 2.10 and Theorem 3.1. The latter is an application of Theorem 2.1 involving the prime numbers.