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    Real Analysis : Sequences

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    Give an example of each of the following, or argue that such a request is impossible:
    1) A sequence that does not contain 0,1 as a term but contains subsequences converging to each of these values.

    2) A monotone sequence that diverges but has a convergent subsequence.

    3) A sequence that contains subsequences converging to everypoint in the infinite set{1,1/2,1/3,1/4,...}.

    4) An unbounded sequence with a convergent subsequence.

    5) A sequence that has a subsequence that is bounded but contains no subsequence that converges.

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    Solution Summary

    Real analysis problems involving sequences are solved. The solution is detailed and well presented.