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Math Help - A guess of series

  1. #1
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    Post A guess of series

    Whether the series \sum_{n=1}^{\infty}a_{n} convergence or not ,
    can we get the conclusion \sum_{n=1}^{\infty}o(a_{n}) = o(\sum_{n=1}^{\infty}a_{n})?
    can someone give a prove of it or a counter-example?
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  2. #2
    MHF Contributor

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    Quote Originally Posted by Xingyuan View Post
    Whether the series \sum_{n=1}^{\infty}a_{n} convergence or not ,
    can we get the conclusion \sum_{n=1}^{\infty}o(a_{n}) = o(\sum_{n=1}^{\infty}a_{n})?
    can someone give a prove of it or a counter-example?
    What is o(\sum_{n=1}^{\infty}a_{n}) supposed to mean? (the little o notation is indexed by a variable, like o_n(a_n) in the left hand side, so what should the variable be here??)
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