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Math Help - Sequence and limit

  1. #1
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    Sequence and limit

    Let xn be a sequence of real numbers satisfying xn+1≤xn for n=1,2,...
    Assume there is a constant c such that xn>c-1/n.
    Show that l=lim(xn) exists and l>c
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  2. #2
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    Quote Originally Posted by ashamrock415 View Post
    Let xn be a sequence of real numbers satisfying xn+1≤xn for n=1,2,...
    Assume there is a constant c such that xn>c-1/n.
    Show that l=lim(xn) exists and l>c


    \{x_n\} is a monotone decreasing sequence, and as c-\frac{1}{n}\geq c-1 , we get that this sequence is bounded from below

    and thus \lim\limits_{n\to\infty}x_n exists.

    All is left is to show that c is actually this sequence's infimum...

    Tonio
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