$$\lim_{n\to\infty} \sum_{k=1}^{n} \left( \frac{1}{k^2} \cdot \int_{0}^{1} \frac{x^k(1-x)}{1+x^2} dx \right) \cdot \left( \sum_{m=1}^{k} \frac{1}{m} \right)$$
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