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Homework Help: Direct Comparison Test inequality help

  1. Jul 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Explain why the Direct Comparison Test allows us to use the inequality Ln n < n^(1/10) even though it is not true for a great many n values.

    2. Relevant equations



    3. The attempt at a solution
    I looked at the graphs of Ln (n) vs. n^(k)
     
  2. jcsd
  3. Jul 13, 2010 #2

    Mark44

    Staff: Mentor

    Re: Dct

    And what did you find out?

    Also, how did you graph nk?
     
  4. Jul 13, 2010 #3
    Re: Dct

    Actually, ln n < n^{1/10} is only true for n < 3 (for integer values of n).
     
  5. Jul 13, 2010 #4

    Mark44

    Staff: Mentor

    Re: Dct

    That is incorrect. The statement ln n < n.1 is true for n = 3, and it is also true for a lot of much larger values.

    In this problem you're supposed to provide justification for the assertion that ln n < n.1 for some infinitely long interval.
     
  6. Jul 13, 2010 #5
    Re: Dct

    Thanks. Just realized I have been looking at the question the wrong way
     
  7. Jul 13, 2010 #6
    Re: Dct

    Just plotted the graph
     
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