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Math Help - Find an example of a sequence

  1. #1
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    Find an example of a sequence

    Find an example of a non-negative sequence \{a_n\} such that \textstyle \sum a_n^2 converges but \textstyle \sum \frac {a_n} n diverges.

    I only know what it cannot be. It cannot be \frac 1 {n^s} for any real s, it cannot be \frac 1 {log^s n} for any real s, and obviously any geometric series won't work...

    I'm stuck. I would appreciate a hint.
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  2. #2
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    Re: Find an example of a sequence

    Scratch that... I thought it was possible, but I think I just proved that such a sequence is impossible.
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