Let $S$ be a finite set of positive integers such that none of them has a prime factor greater than three. Show that the sum of the reciprocals of the elements in $S$ is smaller than three.
Source: MOP 2005 Homework - Red Group #5
Tags: algebra solved, algebra
Let $S$ be a finite set of positive integers such that none of them has a prime factor greater than three. Show that the sum of the reciprocals of the elements in $S$ is smaller than three.