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Prove that the lim of the sequence (S_n)=0

  1. Oct 6, 2012 #1
    1. The problem statement, all variables and given/known data
    suppose that (s_n) and (t_n) are sequences in which abs(s_n)≤t_n for all n and let lim(t_n)=0. Prove that lim (s_n)=0.






    3. The attempt at a solution
    I find absolute values to be really sketchy to work with I'm really in the dark if this is at all correct:

    Let ε>0 be given, then -ε<(t_n)<ε for some n>N since the limit exists. Since -t_n≤ s_n ≤ t_n for all we can say that for -ε<-t_n≤ S_n≤t_n<ε for n>N above. hence lim(S_n)=0.




    If you have any suggestion about how to deal with the absolutes in a general manner in these kind of proofs I'd be happy to hear it.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 6, 2012 #2

    Zondrina

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    Homework Helper

    Ahh now there's a very nice trick you can apply here. Recall the squeeze theorem works the same way it does for functions as it does for sequences.

    So :

    |sn| ≤ tn

    Tells us that :

    -tn ≤ sn ≤ tn
     
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