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The series diverges by the Ratio Test.
(1) If , then converges (absolutely).
(2) If , then diverges.
(3) If , then the Ratio Test is inconclusive.
Note: In general, Ratio Test is inconclusive (thus not applicable) if there is variable in the exponent (i.e., there is no th power).
Let's test the convergence of the series by using the Ratio Test:
Therefore, the Ratio Test is conclusive for this series - it is divergent.
We need to determine if the Ratio Test is Inconclusive to the given series.
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