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21434product convergence

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  • tsr21
    May 3, 2010
      Hi all,

      A correspondent has asked me about the infinite product (p-2)/p where p is a prime from 5 to infinity. So the first few terms are
      3/5, 5/7, 9/11, 11/13, 15/17 etc.

      Clearly the terms converge to 1, and the product - 3/5, then 3/7, then 27/77, then 27/91, etc - also converges. But does the product converge to zero, or to a small but finite number?

      I have been unable to answer him definitively. Can anyone else here do so?

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