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 not using the Comparison Test (NOT the Limit Comparison Test.) For each statement, enter C (for 'correct") if the argument is valid, or enter I (for "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 I.) For all n > 1, arctan(n)/n^3 2, in (n)/n^2 > 1/n^2, and the series sigma 1/n^2 converges, so by the Comparison Test, the series sigma in (n)/n^2 converges. For all n > 1, n/6 - n^3 1, sin^2 (n)/n^2 2, 1/n^2 - 5 2, squareroot n +1/n > 1/n, and the series 1/n converges, so by the Comparison Test, the series sigma squareroot n +1/n diverges.

Explanation / Answer

1. The statement is correct. By comparison test.

2.The statement is Incorrect. As the divergence of smaller series implies the divergence of the bigger series.

3.The statement is correct. By comparison test.

4.The statement is Correct.

5. The statement is Correct

6. The statement is Correct

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