Each of the following statements is an attempt to show that a given series is co

Question

Each of the following statements is an attempt to show that a given series is convergent or divergent using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter or "correct") if the argument is valid, or enter (or "incorrect" if any part of the argument is flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter .) 1. For all n > 1 1 , and the series converges, so by the Comparison Test, the series -converges. In(n) 3.Foralin > 2 Inn-12, andthe series 1n(r) and the series converges, so by the Comparison Test, the series 4. For alln 2 > -' and the series - diverges, so by the Comparison Test, the series -diverges. 2+ sin2(n) and the series 3 2 + sin2(r) 2 5. For all n1, 2converges, so by the Comparison Test, the series converges. 2 nan9 converges. 6. For all n > 2, and the series 2 2 converges, so by the Comparison Test, the series

Explanation / Answer

1)CONVERGES-----CORRECT

2) CONVERGES----CORRECT

3)CONVERGES----CORRECT

4)DIVERGES----CORRECT

5)CONVERGES---CORRECT

6)CONVERGES---CORRECT

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