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Math Help - General Question About Sequences

  1. #1
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    General Question About Sequences

    Is it okay to use Comparison Theorem to prove that a sequence converges? I would think so, but I recall my professor commenting on that in class by saying that it works with series. I don't know whether or not he meant that to exclude sequences.

    If not, why doesn't it work? I appreciate the help!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Hikari View Post
    Is it okay to use Comparison Theorem to prove that a sequence converges? I would think so, but I recall my professor commenting on that in class by saying that it works with series. I don't know whether or not he meant that to exclude sequences.

    If not, why doesn't it work? I appreciate the help!
    The comparison test works with series, not sequences.

    to see that it does not work in general for sequences, consider the following two sequences

    \{ a_n \} = 2,2,2,2,2 ... and

    \{ b_n \} = -1,1,-1,1,...

    note that |b_n| \le |a_n| for all n and \{ a_n \} converges. Yet, \{ b_n \} does not converge
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  3. #3
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    Thanks so much!
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