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Binomial Theorem related proofs

  1. Dec 5, 2011 #1
    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[itex]\in[/itex]N with n[itex]\geq[/itex]M, show that (a^n)/(n!)[itex]\leq[/itex]((a/M)^(n-M))*(a^M)/(M!)
    b)Use the previous prblem 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
    I just don't really know where to start. Any hints? or suggestions?
     
  2. jcsd
  3. Dec 5, 2011 #2

    HallsofIvy

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