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Limit of a strange sequence

  1. Sep 24, 2009 #1

    JJ6

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    1. The problem statement, all variables and given/known data

    I need to find the limit of the sequence:

    [(1+1/n)(1+2/n)(1+3/n)...(1+n/n)]^(1/n) as n approaches infinity.

    I know that the limit should come out to 4/e, but I cannot figure out why.

    2. Relevant equations

    None.

    3. The attempt at a solution

    The original sequence is equivalent to [(2n)!/(n!*n^n)]^(1/n), but I have absolutely no idea what to do with it after that. Can anybody point me in the right direction?
     
  2. jcsd
  3. Sep 24, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    Why not just apply Stirling's approximation to the original sequence?
     
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