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Math Help - monotone sequences

  1. #1
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    monotone sequences

    Let (An) and (Bn) be monotone sequences. Prove or give a counter example
    A) The sequence (Cn) given by Cn = KAn is monotone for any k element of R
    B) The sequence (Cn) given by Cn = An/Bn is monotone.
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  2. #2
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    Quote Originally Posted by luckyc1423 View Post
    Let (An) and (Bn) be monotone sequences. Prove or give a counter example
    A) The sequence (Cn) given by Cn = KAn is monotone for any k element of R
    B) The sequence (Cn) given by Cn = An/Bn is monotone.
    a_n is either:
    a_1<=a_2<=a_3<=...
    Or,
    a_1>=a_2>=a_3>=...

    If k=0 nothing to proof. (Why?)
    If k>0 then,
    ka_1<=ka_2<=ka_3<=...
    Or,
    ka_1>=ka_2>=ka_3>=...

    If k<0 then,
    ka_1>=ka_2>=ka_3>=...
    Or,
    ka_1<=ka_2<=ka_3<=...

    All cases covered.
    Q.E.D.

    Second one is NO.
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