Use the Ratio Test to determine whether the series converges absolutely or diverges. $$ \sum_{k=1}^{\infty} \frac{2^k}{3^k} $$ Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer in simplified form.) A. The series converges absolutely because r = B. The series diverges because r = C. The Ratio Test is inconclusive because r =
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The given series is $$ \sum_{k=1}^{\infty} \frac{2^k}{3^k} $$. We need to use the Ratio Test. Show more…
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Use the Ratio Test or the Root Test to determine whether the following series converges absolutely or diverges. Select the correct choice below and fill in the answer box within your choice: A. The series diverges by the Root Test because ρ = . B. The Root Test is inconclusive because ρ = . C. The Ratio Test is inconclusive because r = . D. The series diverges by the Ratio Test because r = . E. The series converges absolutely by the Ratio Test because r = . F. The series converges absolutely by the Root Test because ρ = .
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