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