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Inf{a^n: n in Z+}=0

  1. Dec 21, 2008 #1
    Given "a" with 0<a<1, prove that inf{a^n : n in Z+}=0

    [HINT] Let h=(1-a)/a , show (1+h)^n >= 1 +nh


    I have proven the second part of the hint using induction but I cannot figure out why this shows the statement holds.

    I have gotten that the hint is the same as,

    a^-n >= 1+nh , I don't know what I am not seeing.

    Again, thank you in advance.
     
  2. jcsd
  3. Dec 21, 2008 #2

    Dick

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    1+nh goes to infinity as n->infinity. That means a^(-n) goes to infinity. a^(n)=1/a^(-n). So?
     
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