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- Apr 18th 2011, 11:30 AMBruno J.Prove this limit
- Apr 18th 2011, 05:10 PMKrizalid
About the power involved there, I think it covers the whole product.

http://www.fmat.cl/tex/e60391cea26df...7ebd0da39a.png

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.) - Apr 21st 2011, 10:48 AMBruno J.
Good solution! I don't see any ambiguity about the exponent applying to the whole product or not, though. :)

- May 13th 2011, 04:03 AMsakodo
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.

- May 13th 2011, 05:28 AMgirdav
If you write the second product as $\displaystyle \prod_{j=1}^n\frac jn$ you will get the $\displaystyle \frac 1n$ because it doesn't depend on $\displaystyle i$.

- May 13th 2011, 05:44 AMsakodo
When you bring the $\displaystyle \frac{1}{n^2}$ in, wouldn't you get -$\displaystyle \frac{1}{n^2}$ $\displaystyle \sum_{i=1}^n$ln$\displaystyle \frac{i}{n}$ ? How did the $\displaystyle \frac{1}{n}$ vanish?