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Percise defination of the limit of a sequence problem

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data

    it is shown that lim n->Infinity of ln(n)/n=0
    Find a natural number N such that
    n> N -> |ln(n)/n - 0| < 1/10


    3. The attempt at a solution

    A sequence has a limit 0 if for every [tex]\epsilon[/tex]>0 there exists a number N such that for every n > N

    |ln(n)/n-0|<[tex]\epsilon[/tex]

    Take [tex]\epsilon[/tex]=1/10, as ln(n)/n > 0 for any sufficently large n we have

    ln(n)/n < 1/10.

    so I choose N=10ln(n).

    My problem starts here this is a function of a variable being sent to infinity I am not sure how exactly one solves for N that is purely a function of [tex]\epsilon[/tex].
     
  2. jcsd
  3. Feb 12, 2008 #2
    You can find any natural number, so just get an upper bound for ln(n).

    For example, ln(n) < sqrt(n)
     
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