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Math Help - limit superior and limit inferior

  1. #1
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    limit superior and limit inferior

    I dont understand limit superior and limit inferior. I know what the definitions are but I would not know how to apply it in an example since my teacher did not explain how to go about that. How would I find the limit superior and limit inferior of {(n/3)-[n/3]}?
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by summerset353 View Post
    I dont understand limit superior and limit inferior. I know what the definitions are but I would not know how to apply it in an example since my teacher did not explain how to go about that. How would I find the limit superior and limit inferior of {(n/3)-[n/3]}?
    I'll show you one part. You show me another. I assume that this is a_n=\frac{n}{3}-\left\lfloor \frac{n}{3}\right\rfloor. Clearly, we have that a_n\geqslant 0 and so \liminf\text{ }a_n\geqslant 0 but considering that a_{3n}=0 we see that \liminf\text{ }a_n=0.
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