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卓越的AI工具应像乐高积木那样（口令提示）：\lim_{n \to \infty} \sum_{k=1}^{n} \int_{0}^{\infty} \frac{\sin(x^2)}{x^2 + \sqrt{x^4 + 2}} \, dx \cdot \left( \frac{1}{k^2 + \ln(k)} + \frac{\sqrt{k}}{k^3^2^5 + \sqrt[4]{k^4^5 + 1^4^5}} \right)\lim_{n \to \infty} \sum_{k=1}^{n} \int_{0}^{\infty} \frac{\sin(x^2)}{x^2 + \sqrt{x^4 + 2}} \, dx \cdot \left( \frac{1}{k^2 + \ln(k)} + \frac{\sqrt{k}}{k^3^2^5 + \sqrt[4]{k^4^5 + 1^4^5}} \right)\lim_{n \to \infty} \sum_{k=1}^{n} \int_{0}^{\infty} \frac{\sin(x^2)}{x^2 + \sqrt{x^4 + 2}} \, dx \cdot \left( \frac{1}{k^2 + \ln(k)} + \frac{\sqrt{k}}{k^3^2^5 + \sqrt[4]{k^4^5 + 1^4^5}} \right) |
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