# Binomial Theorem related proofs

1. Dec 5, 2011

### h.shin

1. The problem statement, all variables and given/known data
Let a be a fixed positive rational number. Choose(and fix) a naural number M > a.
a) For any n$\in$N with n$\geq$M, show that (a^n)/(n!)$\leq$((a/M)^(n-M))*(a^M)/(M!)
b)Use the previous prblem to show that, given e > 0, there exists an N$\in$$N$ such that for all n$\geq$N, (a^n)/(n!) < e

2. Relevant equations

3. The attempt at a solution
I just don't really know where to start. Any hints? or suggestions?

2. Dec 5, 2011

### HallsofIvy

Start by looking at simple examples. What if, say, a= 1/2, M= 1 and n= 2? What if M= 2 and n= 2?