(adsbygoogle = window.adsbygoogle || []).push({}); 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Difficult series convergence proof

**Physics Forums | Science Articles, Homework Help, Discussion**