In the first part of the question, I proved that(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_{1/2}^{2} \frac{ln x}{1+x^2} dx = 0 [/tex]

Then I needed to evaluate the following but I didn't know how to do it. Can you give me some clues? I know it must be related to the definite integral that I proved in the first part, but how?

[tex]\lim_{n\rightarrow\infty} \sum_{k=1}^{3n} \frac{ln (2( \frac{1}{2} + \frac{k}{2n}))}{2n (1 + ( \frac{1}{2} + \frac{k}{2n})^2)} [/tex]

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# Sum an infinite series by definite integrals

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