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Math Help - Sequence question

  1. #1
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    Sequence question

    Hi

    A sequence is defined by
    A = (-1)^n * [n/n+1]

    What is the limit of the sequence? I know that this is an oscilating sequence (-1 and 1) but my teacher today told that its "LIMIT" was 0. I was not able to grasp the concept at all and somehow i dont trust my teacher too much.

    can anyone help me out in this ?

    thanks
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  2. #2
    MHF Contributor red_dog's Avatar
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    \lim_{n\to\infty}a_{2n}=\lim_{n\to\infty}\frac{2n}  {2n+1}=1

    \lim_{n\to\infty}a_{2n+1}=\lim_{n\to\infty}\left(-\frac{2n+1}{2n+2}\right)=-1

    So, the sequence (a_n) has two subsequences that have different limits. Then (a_n) has no limit.
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