# Thread: Limit Problem

1. ## Limit Problem

Hi everyone.
I've tried to solve this limit; but I really don't know how to treat it.
$\displaystyle \lim_{n \rightarrow\infty} \sum_{i=1}^n \frac{n}{n^2 + i^2}$
I appreciate your help.
everk.

2. Originally Posted by everk
Hi everyone.
I've tried to solve this limit; but I really don't know how to treat it.
$\displaystyle \lim_{n \rightarrow\infty} \sum_{i=1}^n \frac{n}{n^2 + i^2}$
I appreciate your help.
everk.
Are you studying the Riemann integral by any chance? Divide top and bottom of that sum by $n^2$ so that it becomes $\displaystyle\frac1n \sum_{i=1}^n \frac{1}{1 + (i/n)^2}$, and think of that as a Riemann sum for an integral.