A limit on binomial coefficients Let $$x_n=\frac{1}{n^2}\sum_{k=0}^n \ln\left(n\atop k\right).$$ Find the limit of $x_n$.
What I can do is just use Stolz formula. But I could not proceed.

For a two terms estimate of the behaviour of $\displaystyle\prod_{k=0}^{n}\binom{n}{k}$ one can check out March 2013 volume of Asymmetry problem V2-4 here (http://akotronismaths.blogspot.gr/p/asymmetry-electronic-mathematical.html)
