(1 point) Match the following series with the series below in which you can compare using the Limit Comparison Test. Then determine whether the series converge or diverge. A. sum_{n=1}^{infty} frac{1}{n}, B. sum_{n=1}^{infty} frac{1}{n^2}, C. sum_{n=1}^{infty} frac{1}{n^3}, and D. sum_{n=1}^{infty} frac{1}{sqrt{n}} 1. B sum_{n=1}^{infty} frac{1}{n^2 + n + 1} Does this series converge or diverge? Converges 2. C sum_{n=1}^{infty} frac{1}{2n^3 + 8} Does this series converge or diverge? Converges 3. B sum_{n=2}^{infty} frac{1}{2n - sqrt{n}} Does this series converge or diverge? Diverges 4. D sum_{n=2}^{infty} frac{sqrt{n}}{n - 1} Does this series converge or diverge? Diverges
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The series ∑ (n^2 + n + 1) from n=1 to infinity can be compared to the series ∑ n^2 from n=1 to infinity. The limit comparison test gives us the limit as n approaches infinity of (n^2 + n + 1) / n^2 = 1 + 1/n + 1/n^2, which approaches 1. Since the series ∑ n^2 is Show more…
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