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Math Help - Conditional and absolute convergence

  1. #1
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    Conditional and absolute convergence

    For each y \in (0,1], find a series of the form \sum\limits_{n=1}^{\infty}{a_nn^{-x}} which is absolutely convergent for x>1 but not for x<1 and is (conditionally) convergent for x>y but not for x<y.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Newtonian View Post
    For each y \in (0,1], find a series of the form \sum\limits_{n=1}^{\infty}{a_nn^{-x}} which is absolutely convergent for x>1 but not for x<1 and is (conditionally) convergent for x>y but not for x<y.
    Is the sequence supposed to depend on y?
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  3. #3
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    Yes; we may assume we're given a y \in (0,1] and we want to find a series as stated (by defining a_n, which are allowed to depend on the given y).
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