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I have a problem to show that:

$$\lim_{x \to0^+} \sum_{n=1}^{\infty} \frac{2x}{n^2x^2+1} = \pi$$

any help is greatly appreciated.

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you might find this link helpful: math.stackexchange.com/questions/3525/… ,divide left side by $z^2$ –  Ziqian Xie Mar 30 at 14:54

1 Answer 1

up vote 4 down vote accepted

Rename $x$ as $\Delta x$. That may help you to see that your limit is $\int_0^\infty{f(x)\,dx}$, where $f(x) = {2\over x^2+1}$. (You should recognize your limit as the limit of a Riemann sum.)

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Now I see, thank you : ) –  Prold Mar 30 at 15:39
    
Great, glad to help –  Jason Zimba Mar 30 at 22:35

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