It seems that $$\lim_{x->\infty}\sum_{n=-\infty}^{\infty}\frac{x}{n^2+x^2}=\pi$$ But I can't prove it. I cannot prove that the function is decreasing in $x$ either.
Is $\lim_{x->\infty}\sum_{n=-\infty}^{\infty}\frac{x}{n^2+x^2}=\pi$?
Yaakov Baruch
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