Problem 3. (20 points) Determine whether the following series converge absolutely, con-verge conditionally, or diverge. Show all work to justify your answers. \sum_{n=1}^{\infty} \frac{(-1)^{n}(3 n+1)}{n^{2}+2 n} \sum_{n=2}^{\infty} \frac{\sin (n)+1}{n^{2} \ln n}

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