I need to find a Riemann Integral corresponding to this limit
$$ \lim_{n->inf}\sum_{r=1}^n\frac{n}{n^2+r^2} $$
I tried equating the fraction to a $\frac{b-a}{n}f(x_r)$ where $x_r=a+r(\frac{b-a}n)$ but I can't seem to be able to find f(x) at all.
2026-03-30 08:01:27.1774857687
Find a Riemann Integral given the limit of a sum
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Hint: Rerwite the fraction by multiplying both the numerator and denominator by $1/n^2$. This gives $$\frac1n\frac{1}{(r/n)^2+1}.$$
It should be a lot easier to recognize this as a Riemann sum.