Limit of sum of the series What would be the sum of following ?
$$\lim_{n\to\infty} \left[\frac{1}{(n+1)^{2}} + \frac{1}{(n+2)^{2}} + \frac{1}{(n+3)^{2}} + \cdots + \frac{1}{(n+n)^{2}}\right]$$
I tried to turn it into integral : 
$\displaystyle\int \frac{1}{(1+\frac{r}{n})^{2}}\frac{1}{n^{2}} $ but 
I can't figure out how to deal with $\frac{1}{n^{2}}$

The series $\sum_{j=}^{\infty}1/j^2$ converges by the Cauchy condensation test so $0<\sum_{j=n}^{j=2 n}1/j^2 < \sum_{j=n}^{\infty}1/j^2$ which $\to 0$ as $n\to \infty.$
