# Prove this limit

• April 18th 2011, 12:30 PM
Bruno J.
Prove this limit
• April 18th 2011, 06:10 PM
Krizalid
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.)
• April 21st 2011, 11:48 AM
Bruno J.
Good solution! I don't see any ambiguity about the exponent applying to the whole product or not, though. :)
• May 13th 2011, 05:03 AM
sakodo
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, 06:28 AM
girdav
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 $i$.
• May 13th 2011, 06:44 AM
sakodo
When you bring the $\frac{1}{n^2}$ in, wouldn't you get - $\frac{1}{n^2}$ $\sum_{i=1}^n$ln $\frac{i}{n}$ ? How did the $\frac{1}{n}$ vanish?