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Math Help - Prove this limit

  1. #1
    MHF Contributor Bruno J.'s Avatar
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    Prove this limit



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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    About the power involved there, I think it covers the whole product.



    Where it says "lím" is because I took it from a spanish forum, but it clearly means "limit."

    (You can solve the double integral as you please.)
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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    Good solution! I don't see any ambiguity about the exponent applying to the whole product or not, though.
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  4. #4
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    Hi guys can anyone please explain the fourth line? I don't understand how you get 1/n in the negative part. I keep getting 1/n^2. Many thanks.
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  5. #5
    Super Member girdav's Avatar
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    If you write the second product as \prod_{j=1}^n\frac jn you will get the \frac 1n because it doesn't depend on i.
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  6. #6
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    When you bring the \frac{1}{n^2} in, wouldn't you get - \frac{1}{n^2} \sum_{i=1}^nln \frac{i}{n} ? How did the \frac{1}{n} vanish?
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