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Math Help - Real Analysis Question 5 - Sequence Convergence

  1. #1
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    Real Analysis Question 5 - Sequence Convergence

    Hello again. This is the final question that I have for now.

    Argue that the sequence

    1,0,1,0,0,1,0,0,0,1,0,0,0,0,1, 5 zeros,1...

    does not converge to zero. For what values of ε > 0 does there exist a response N? For which values of ε > 0 is there no suitable response?

    Any help on this would be greatly appreciated. Thanks.
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  2. #2
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    For any epsilon less than 1, and any number N, there will always come a 1, which is not in the neighborhood of epsilon around 0.
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