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Math Help - Intro to Real Analysis.

  1. #1
    Member ilikedmath's Avatar
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    Exclamation Intro to Real Analysis.

    The problem asks for us to: Construct a sequence { s_n} for which the subsequential limits are {- \infty, -2, 1}.

    I found some help already:
    ...the sequence {-n} has the subsequential limit of {- \infty},
    ...the sequence is {-2 - 1/n} has the subsequential limit of {-2}, and
    ... the sequence {1 - 1/n} has the subsequential limit of {1}.

    How do I combine the three sequences to make the one sequence I need for the problem.

    Any help, suggestions, corrections, and tips of any kind are greatly appreciated.
    Thank you for your time!
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle s_n=\left\{\begin{array}{lll}-n & ,n=3p\\-2-\frac{1}{n} & ,n=3p+1\\1-\frac{1}{n} & ,n=3p+2\end{array}\right.
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  3. #3
    Member ilikedmath's Avatar
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    Question

    Quote Originally Posted by red_dog View Post
    \displaystyle s_n=\left\{\begin{array}{lll}-n & ,n=3p\\-2-\frac{1}{n} & ,n=3p+1\\1-\frac{1}{n} & ,n=3p+2\end{array}\right.
    Awesome, our professor did give a hint to go 'piecewise' with this problem.
    My only question is, where'd the '3p' come from? I understand that 3p, 3p + 1, and 3p + 2 are three consecutive terms.
    Last edited by ilikedmath; November 15th 2008 at 05:48 AM.
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