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Cant understand how they use a theorem question

  1. Mar 12, 2009 #1
    http://www.freeimagehosting.net/uploads/th.38f39915df.gif

    i marked a place where they use theorem 4

    but theorem 4 talks about that if one sequence is bigger then the other
    then so is their liminf and limsup
    it doesnt tell anything about the limsup of the sum of the sequences


    i cant understand how they use this fact for getting the marked result
    what does theorem 4 has to do with the limsup of the sum of sequences
    ??


    how they made that step?
     
    Last edited: Mar 13, 2009
  2. jcsd
  3. Mar 12, 2009 #2
    Let [tex]\alpha_n = a_n+b_n,\ \beta_n = a+b+\epsilon[/tex](constant) and apply theorem 4 for the sequences [tex]\alpha_n[/tex] and [tex]\beta_n[/tex] and you will get the result.
     
  4. Mar 12, 2009 #3
    i cant see how i get the supreme of the sum of both sequences
    using theorem 4

    ??
     
  5. Mar 12, 2009 #4
    theorem 4 talks about that if one sequence is bigger then the other
    then so is the liminf of the first is bigger then the other and so is for limsup
    it doesnt tell anything about the limsup of the sum of the sequences
    ??
     
  6. Mar 13, 2009 #5
    i cant understand what you are saying
    how ill get the result
    /??
     
  7. Mar 13, 2009 #6
    why a_n +b_n =limsup(a_n +b_n)
    ??
     
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