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Homework Help: Proving a limit

  1. Sep 18, 2007 #1
    1. The problem statement, all variables and given/known data


    Prove that lim x_n = 0 as n approaches infinity

    2. Relevant equations

    E > 0

    3. The attempt at a solution

    There is a natural number N such that N>1/sqrt(E). There is also a number n>N>1/sqrt(E) <==> sqrt(n)>1/sqrt(sqrt(E)) ==> E>sqrt(sqrt(E))>1/sqrt(n). If this last inequality is correct, I can prove the limit in question. But it can't be, because E<sqrt(sqrt(E)) if 0<E<1. So, what should I do instead?
  2. jcsd
  3. Sep 18, 2007 #2


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    Science Advisor
    Homework Helper

    You've got this all twisted around. You want 1/sqrt(n)<E for n>N. So you want N>1/E^2.
  4. Sep 19, 2007 #3
    I see; it's N I'm after. Thank you!
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