Re: limit of a sequence

In article <468f80a8$0$36439$4fafbaef@xxxxxxxxxxxxxxxxxxx>, Armando C.
<xxxxxxxxxxx@xxxxxxxxx> wrote:

I've a doubt about the following sequence limit, I tried many times
to solve it, but I couldn't work it out.


lim n->+inf ( 1/(n^2+n+1) + 2/(n^2+n+2) + ..... + n/(n^2+n+n))

My book says result is 1/2, but frankly speaking I don't understand
how it comes to it. If each term is infinitesimal how can sum be
different from 0?

Thanks in advance.




The terms get small, but the number of terms gets large.
.