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Does limit ln(n)/n^c -> 0 for any c>0?

  1. Oct 8, 2010 #1
    1. The problem statement, all variables and given/known data

    Does limit ln(n)/n^c -> 0 for any c>0?

    2. Relevant equations

    3. The attempt at a solution
    I wonder if there is an
    1.Epsilon Delta Proof
    2.Proof using BigO SmallO notation.

  2. jcsd
  3. Oct 8, 2010 #2
    It is obviously true. There are a lot of ways to prove this. What kind of class is this for? Are you expected to be rigorous in your solutions? N-epsilon proofs and asymptotic behaviour are very different arguments in terms of the development required in an analysis setting.
  4. Oct 8, 2010 #3
    Yes, this is for real analysis class
  5. Oct 8, 2010 #4
    What tools do you have available? How was ln(n) derived?

    There is a nifty theorem that says that if a sequence converges then any subsequence will converge to the same limit. This will enable you to look at ln(x)/x^c in R rather than in N.
  6. Oct 8, 2010 #5
    Yes, we can use Bolzano Weierstrasse Theorem. Please feel free to proceed.
    My level is on baby Rudin, the this is the first course in real analysis.
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