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Math Help - Series

  1. #1
    Junior Member
    Joined
    Nov 2005
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    43

    Series

    "Suppose (a_n) is a bounded increasing seq and (b_n) is a bounded decreasing seq. Let x_n=a_n+b_n. Show that \sum|x_n-x_{n+1}| converges."

    Triangle ineq yields

    \sum|x_n-x_{n+1}|\leq \sum|a_n-a_{n+1}| + \sum|b_n-b_{n+1}|

    from which point I am unable to deduce that either of the RHS sums converge.
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  2. #2
    Junior Member
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    Nov 2005
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    Got it, thanks.
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