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Divergence?

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  • Werner D. Sand
    sum(1/n - 1/p(n)), n- inf, seems to diverge. But how to prove?
    Message 1 of 2 , May 2, 2006
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      sum(1/n - 1/p(n)), n->inf, seems to diverge. But how to prove?
    • jbrennen
      ... Easily. Show that for some positive constant C, we have: 1/n - 1/p(n) = C/n Then your sum exceeds the infinite sum of C/n, which diverges for any
      Message 2 of 2 , May 2, 2006
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        --- In primenumbers@yahoogroups.com, "Werner D. Sand" <Theo.3.1415@...>
        wrote:
        >
        > sum(1/n - 1/p(n)), n->inf, seems to diverge. But how to prove?
        >

        Easily. Show that for some positive constant C, we have:

        1/n - 1/p(n) >= C/n

        Then your sum exceeds the infinite sum of C/n, which diverges
        for any positive C.
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