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Rules for monotone sequences?

  1. Jun 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Let an be monotone sequences. Prove or give a counterexample:

    The sequence cn given by cn=k*an is monotone for any Real number k.

    The sequence (cn) given by cn=(an/bn) is monotone.

    2. Relevant equations



    3. The attempt at a solution

    On the first one, I don't think the change of sign on k can change the "monotoneness" of the sequence other than by changing decreasing to increasing and vice versa.

    I have played around using different sequences to see if this is true and it is looking like it is, but I just feel that it could be false.

    Any ideas?
     
    Last edited: Jun 30, 2011
  2. jcsd
  3. Jun 30, 2011 #2

    lanedance

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    Homework Helper

    for the first calculate the difference between terms and show it is always either pos or neg

    2nd find a simple counter example, consider an alternating series
     
  4. Jun 30, 2011 #3
    I neglected to put the condition that bn is also monotone.

    So I was thinking of an with a different sign than bn but this doesn't seem to change much either.
     
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