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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 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.) In(n) 1 In(n) 1. For all n > 1, n2 i5, and the series 2 converges, so by the Comparison Test, the series 2 converges. n2 n15 n1.5 1 2. For all n > 2, n2 -6 and the series 24 converges, so by the Comparison Test, the series 1 n2 converges. n2 n2-6 In(n) 3. For all n > 2, n2 In(n) , and the series converges, so by the Comparison Test, the series E converges. n? n2 n2 1 4. For all n > 1, 2, and the series 2 E diverges, so by the Comparison Test, the series > n In(n) diverges. n In(n) n 2 5. For all n > 2, n3-3 and the series 2 converges, so by the Comparison Test, the series 2", converges. n2 n2 n3 –3 arctan(n) arctan(n) 6. For all n > 1 and the series 2+ converges, so by the Comparison Test, the series 2 n3 converges. n3 2n3 n3

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 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.) In(n) 1 In(n) 1. For all n > 1, n2 i5, and the series 2 converges, so by the Comparison Test, the series 2 converges. n2 n15 n1.5 1 2. For all n > 2, n2 -6 and the series 24 converges, so by the Comparison Test, the series 1 n2 converges. n2 n2-6 In(n) 3. For all n > 2, n2 In(n) , and the series converges, so by the Comparison Test, the series E converges. n? n2 n2 1 4. For all n > 1, 2, and the series 2 E diverges, so by the Comparison Test, the series > n In(n) diverges. n In(n) n 2 5. For all n > 2, n3-3 and the series 2 converges, so by the Comparison Test, the series 2", converges. n2 n2 n3 –3 arctan(n) arctan(n) 6. For all n > 1 and the series 2+ converges, so by the Comparison Test, the series 2 n3 converges. n3 2n3 n3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 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.) In(n) 1. For all n > 1, n2 In(n) converges. 1 1 and the series converges, so by the Comparison Test, the series 2 n1.5 n1.5 n2 1 and the series 2 n2 1 converges. 1 2. For all n > 2, n² –6 In(n) 3. For all n > 2, n2 1 n2 converges, so by the Comparison Test, the series 2 n2 -6 In(n) converges. 1 and the series2 converges, so by the Comparison Test, the series 2 n2 n2 1 4. For all n > 1, and the series 22; diverges, so by the Comparison Test, the series 2 1 diverges. n In(n) n In(n) n 5. For all n> 2, 2 and the series 2 2 + n2 n converges, so by the Comparison Test, the series 2". converges. п3 —3 n2 п3 —3 arctan(n) arctan(n) 6. For all n > 1, and the series 2 2n3 converges, so by the Comparison Test, the series 2 n3 converges. n3 n³
Transcribed Image Text: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 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.) In(n) 1. For all n > 1, n2 In(n) converges. 1 1 and the series converges, so by the Comparison Test, the series 2 n1.5 n1.5 n2 1 and the series 2 n2 1 converges. 1 2. For all n > 2, n² –6 In(n) 3. For all n > 2, n2 1 n2 converges, so by the Comparison Test, the series 2 n2 -6 In(n) converges. 1 and the series2 converges, so by the Comparison Test, the series 2 n2 n2 1 4. For all n > 1, and the series 22; diverges, so by the Comparison Test, the series 2 1 diverges. n In(n) n In(n) n 5. For all n> 2, 2 and the series 2 2 + n2 n converges, so by the Comparison Test, the series 2". converges. п3 —3 n2 п3 —3 arctan(n) arctan(n) 6. For all n > 1, and the series 2 2n3 converges, so by the Comparison Test, the series 2 n3 converges. n3 n³
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