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Binomial Theorem related proofs

  1. Dec 6, 2011 #1
    1. The problem statement, all variables and given/known data
    Let a be a fixed positive rational number. Choose (and fix) a natural number M>a.
    Use (a^n)/(n!)[itex]\leq[/itex](a^M/(M!))(a/M)^(n-M) to show that, given e>0, there exists an N[itex]\in[/itex][itex]N[/itex] such that for all n[itex]\geq[/itex]N, (a^n)/n! < e.


    2. Relevant equations



    3. The attempt at a solution
    In a previous problem, I saw that when M>n then (a^n)/(n!)<(a^M/(M!))(a/M)^(n-M). So I thought i could maybe use that to come up with a N in relations to e. but i'm not so sure how to do this. I know the equations are long and ugly, but please help.
     
  2. jcsd
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