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Help with proving a sequence converges

  1. Apr 2, 2009 #1
    I am really stuck on this on

    Let sn and tn be sequences. Suppose that lim sn = L (where s is a real number) and lim |sn - tn| = 0. Prove that lim tn = L.

    I think this is going in the right way but i am not sure. If the lim an = A, then lim |an - A| = 0.

    any help would be very nice.
     
  2. jcsd
  3. Apr 2, 2009 #2
    Help proving a sequesnce converges

    I am really stuck on this on

    Let sn and tn be sequences. Suppose that lim sn = L (where s is a real number) and lim |sn - tn| = 0. Prove that lim tn = L.

    I think this is going in the right way but i am not sure. If the lim an = A, then lim |an - A| = 0.

    any help would be very nice.
     
  4. Apr 2, 2009 #3

    lurflurf

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    let N be so large that
    |s_n|<epsilon/2
    |s_n-t_n|<epsilon
    what can you say about
    |t_n|
    ?
    hint
    |A-B|<=|A|+|B|
     
  5. Apr 3, 2009 #4
    I know how to do a N Epsilon proof but don't you have to have |s_n + t_n - (s + t)| < epsilon??

    And that is to show that the lim (s_n + t_n) = s + t. I need to know lim |s_n - t_n| = 0. i guess i am unsure how the abs effect the proof.
     
  6. Apr 3, 2009 #5

    tiny-tim

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    Homework Helper

    Last edited by a moderator: Apr 24, 2017
  7. Apr 3, 2009 #6

    HallsofIvy

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    Science Advisor

    I have merged the two threads.
     
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