If n is pos. integer, then lim[n->infty](1/n)[(1/n)^2+(2/n)^2+...+((n-1)/n)^2]

[Alek]

Not sure how to start or what to do
The problem is asking this:

If n is a positive integer, then lim n→∞ 1/n[(1/n)^2+(2/n)^2+...+((n-1)/n)^2] can be expressed as...

I'm not sure what to do.

 

[stapel]

Might it help to note that the n's in the denominators in the brackets are all squared and will, for any given n, be fixed, so you can take the 1/n^2 out front? So you end up with:

. . . . .\(\displaystyle \dfrac{1}{n^3}\, [1^2\, +\, 2^2\, +\, 3^2\, ...\, (n\, -\, 1)^2]\)