Finding value of $$\lim_{n\rightarrow \infty}\lim_{m\rightarrow \infty}\sum^{n}_{r=1}\sum^{mr}_{k=1}\frac{m^2n^2}{(m^2n^2+k^2)(n^2+r^2)}$$
what i try
$$\lim_{m\rightarrow \infty}\lim_{n\rightarrow \infty}\sum^{mr}_{k=1}\frac{m^2n^2}{m^2n^2+k^2}\cdot \frac{1}{n}\sum^{n}_{r=1}\frac{n}{n^2+r^2}$$
$$\lim_{n\rightarrow \infty}\sum^{n}_{r=1}\frac{n}{n^2+r^2}=\int^{1}_{0}\frac{1}{1+x^2}dx = \frac{\pi}{4}$$ How do i solve first summation
help me please
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