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The sum $\dfrac{n}{n^2}+\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+ \cdots + \dfrac{n}{n^2+(n-1)^2} + \cdots \cdots$ is

  1. $\frac{\pi}{4}$
  2. $\frac{\pi}{8}$
  3. $\frac{\pi}{6}$
  4. $2 \pi$
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