
> 
> What is the limit, as $n \to \infty$, of the expected distance between two
>  points chosen uniformly at random within a unit edge-length hypercube
>  in $\mathbb{R}^n$?
> 
> 
> 


For $n=1$, the average distance is $\frac{1}{3}$.
For $n=2$, it is approximately $0.52$.
For $n=3$, approximately $0.66$ (Robbins' constant).


But I have not found an expression for arbitrary $n$...



Limit of distance between two random points in a unit $n$-cube
The limit is $\infty$. See equation (2) of <http://mathworld.wolfram.com/HypercubeLinePicking.html>


