1. The problem statement, all variables and given/known data Show that given some ε > 0, there exists a natural number M such that for all n ≥ M, (a^n)/n! < ε 2. Relevant equations 3. The attempt at a solution Ok so I know this seems similar to a Cauchy sequence problem but its not quite the same. So Im looking for a potential value for M that would complete my proof. So far I have found that if M = ε(a^2+1) then it works, through experimenting with different values for a. However, I cannot seem to find a way to show that (a^(M))/M! < ε. Does anyone know a way to do this? Or should I choose a different value for M?