Does the series ?_{n=1}^{?} (-1)? (4 + nĀ³) / n? 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 Comparison Test with ?_{n=1}^{?} 1/n. B. The series converges conditionally per the Alternating Series Test and because the limit used in the Ratio Test is []. C. The series diverges because the limit used in the Ratio Test is not less than or equal to 1. D. The series converges absolutely because the limit used in the nth-Term Test is []. E. The series converges absolutely per the Comparison Test with ?_{n=1}^{?} 4/n?. F. The series diverges because the limit used in the nth-Term Test does not exist.
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The series (-1)^n * 3^n alternates between positive and negative terms. Additionally, the absolute value of each term, |(-1)^n * 3^n|, decreases as n increases. Therefore, the series converges conditionally per the Alternating Series Test. Show moreā¦
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