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Big O Notation Analysis

  1. Sep 22, 2012 #1
    1. The problem statement, all variables and given/known data
    Verify that (n^2 + 3n -3)/n^3 = 0 + O(2/n)


    2. Relevant equations



    3. The attempt at a solution

    I really don't have an attempt. I understand Big O notation, but I don't know how to verify this.
     
  2. jcsd
  3. Sep 22, 2012 #2

    micromass

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    What does the big O notation mean?
     
  4. Sep 22, 2012 #3
    a_n converges to A with a rate of convergence O(b_n). Then you can write a_n=A + O(b_n)
     
  5. Sep 22, 2012 #4

    micromass

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    You still didn't say what "converging with a rate of convergence [itex]O(b_n)[/itex]" means.
     
  6. Sep 22, 2012 #5
    I'm not sure, that's why I'm asking :(
     
  7. Sep 22, 2012 #6
    Big O notation tells you about the leading (that is, largest, or most significant or dominant) contribution to the rate of convergence. Often, the rate of convergence is a sum of terms of the form [itex]n^a[/itex] for some number [itex]a[/itex]. The leading contribution as [itex]n[/itex] gets large comes from the term with the higest value of [itex]a[/itex] because that term will generally be much bigger than all the others.
     
  8. Sep 22, 2012 #7

    micromass

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    What does your book or your notes say?
     
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