Determine whether the alternating series sum_{n=2}^{infty} (-1)^{n+1} frac{3}{7(ln n)^2} converges or diverges. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p-series with p = B. The series does not satisfy the conditions of the Alternating Series Test but diverges by the Root Test because the limit used does not exist. C. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r = D. The series converges by the Alternating Series Test. E. The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p-series with p =
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Determine whether the alternating series ∑_{n=2}^{∑} (-1)^n frac{3}{7(ln n)^2} converges or diverges. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r = . B. The series converges by the Alternating Series Test. C. The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p-series with p = . D. The series does not satisfy the conditions of the Alternating Series Test but diverges by the Root Test because the limit used does not exist. E. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a p-series with p = .
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Determine whether the alternating series converges or diverges. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The series does not satisfy the conditions of the Alternating Series Test but converges because the limit used in the Root Test is . B. The series converges by the Alternating Series Test. C. The series does not satisfy the conditions of the Alternating Series Test but diverges because it is a p-series with r = . D. The series does not satisfy the conditions of the Alternating Series Test but diverges because the limit used in the Ratio Test is . E. The series does not satisfy the conditions of the Alternating Series Test but converges because it is a geometric series with r = .
Does the series sum from n=1 to infinity of (-1)^n * (1 / (n+1)) converge absolutely, converge conditionally, or diverge? Choose the correct answer below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally per the Alternating Series Test and the Limit Comparison Test with sum from n=1 to infinity of (1 / n). B. The series diverges because the limit used in the nth-Term Test is not zero. C. The series converges conditionally because the limit used in the Ratio Test is. D. The series diverges because the limit used in the Ratio Test is not less than or equal to 1. E. The series converges absolutely since the corresponding series of absolute values is the p-series with p =.
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