The first divisible sum (Q1345078)

The authors consider ``the distribution of the first sum of a sequence of positive integer valued i.i.d. random variables which is divisible by \(d\)''. It is known that this sum, divided by \(d\), converges to a geometric distribution as \(d \to \infty\). The rate of convergence is investigated by two methods. The first of them, Stein's method, is based on the coupling technique. The second one uses the theory of Banach algebras. An interesting comparison of the given approaches is presented.