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Analysis help

  1. Jun 14, 2006 #1
    Let (Sn) and (Tn) be sequences such that the lim Sn = +inf and lim Tn > 0

    Then lim SnTn = + inf
  2. jcsd
  3. Jun 14, 2006 #2


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    What is the question? And what work have you done on this problem?
  4. Jun 14, 2006 #3
    A friend of mine, gave it to me.

    I dont know where to start
  5. Jun 14, 2006 #4
    its a statement

    i need a proof
  6. Jun 15, 2006 #5

    matt grime

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    what doyou know about sequences, and multiplication (or division) of sequences?
  7. Jun 15, 2006 #6
    is it

    Let M > 0

    Select a real number m so that 0 < m < limTn.

    There exists an N1 such that:
    n>N1 implies Tn>m

    Since limSn=+inf there exists an N2 such that
    n>N2 implies Sn>(M/m)

    Set N = max{N1,N2}.

    Then n>N imples SnTn>(M/m)*m = M
  8. Jun 15, 2006 #7
    I thought I recognized the wording you used for the statement of this theorem and its proof and sure enough, it is taken word for word out of the book "Elementary Analysis: the Theory of Calculus" by Kenneth Ross (pg 50-51). Its stated with proof as theorem 9.9

    If you have the proof in front of you, why are you asking if thats it? Is there some part of the proof you don't understand?
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