the lim of sum of sequence I have to calculate the following:
$\lim_{n \to \infty} (\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2} + \cdots + \frac{n}{n^2+n^2} )$
I managed to  understand that it is 
$\lim_{n \to \infty} (\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2} + \cdots + \frac{n}{n^2+n^2} ) = \lim_{n \to \infty} \sum_{i=1}^n\frac{n}{n^2+i^2}$
but i can't find a way to calculate...
I found that the sequence lower bound is $\frac{1}{2}$ and upper bound is 1, but thats all...
thanks

Hint: $$\sum \frac{n}{n^2+i^2}=\frac{1}{n}\sum \frac{1}{1+(\frac{i}{n})^2}$$
then use calculus.
