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Re: Divergence?

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  • 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 1 of 2 , May 2, 2006
      --- 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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