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Limit of product of roots

  1. May 4, 2010 #1
    Lt (1 – 1/√2)* (1 – 1/√3)…… (1 – 1/√n+1)
    n->∞


    There must some simple calculation to find this, but I cannot get this, limit exists since

    each tern is less than 1, and limit is more than 0. so limit exists between (1 0).
     
  2. jcsd
  3. May 4, 2010 #2

    tiny-tim

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    Hi bobn! :smile:
    Why?

    Isn't it less than limn->∞ (1 - 1/2)(1 - 1/3)…(1-1/n) ?
     
  4. May 4, 2010 #3
    haa, I am stupid,

    1/√n > 1/n implies, (1- 1/√n) < (1 - 1/n).
     
  5. May 4, 2010 #4
    thx for reply tiny-tim
     
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