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Math Help - Monotone sequence

  1. #1
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    Monotone sequence

    Given y_n=\dfrac12(b+y_n^2) with y_0=0.

    Show that y_n is monotone.

    I'm getting trouble to do that. It's a part of another problem which says to prove that y_n converges, so in order to do that, I already proved that y_n is bounded below.
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  2. #2
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    Do you mean y_{n+1}=\dfrac12(b+y_n^2)?
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  3. #3
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    No, it's as is written.

    Do you think there's a typo?
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  4. #4
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    There must be. Otherwise the sequence is constant for n>0.
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  5. #5
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    A constant sequence is monotonic. And Converges.
    Last edited by Hartlw; April 4th 2011 at 08:10 AM. Reason: add "and converges"
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  6. #6
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    This particular sequence may or may not be monotonic. The given equation may have 2 solutions (depending on b), and therefore the given sequence isn't well defined - it could take on one of these values, or bounce between the 2. In any case, it is more likely that the problem has a typo.
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  7. #7
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    yn is either a real or complex constant depending on b. in either case its constant, monotonic (absoluteley if b complex), and convergent.
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