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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.) 1. For all n > 1, 3-n , and the series converges, so by the Comparison Test, the series E converges. 3-n In(n) n2 In(n) 2. For all n > 1, , and the series converges, so by the Comparison Test, the series converges. In(n) 3. For all n > 2, n2 In(n) converges. , and the series E converges, so by the Comparison Test, the series 1 4. For all n > 1, , and the series 2 E diverges, so by the Comparison Test, the series E n In(n) diverges. n In(n) In(n) 5. For all n > 2, In(n) diverges. , and the series E diverges, so by the Comparison Test, the series n 6. For all n > 2, n2-6 , and the series 2+ converges, so by the Comparison Test, the series converges.

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.) 1. For all n > 1, 3-n , and the series converges, so by the Comparison Test, the series E converges. 3-n In(n) n2 In(n) 2. For all n > 1, , and the series converges, so by the Comparison Test, the series converges. In(n) 3. For all n > 2, n2 In(n) converges. , and the series E converges, so by the Comparison Test, the series 1 4. For all n > 1, , and the series 2 E diverges, so by the Comparison Test, the series E n In(n) diverges. n In(n) In(n) 5. For all n > 2, In(n) diverges. , and the series E diverges, so by the Comparison Test, the series n 6. For all n > 2, n2-6 , and the series 2+ converges, so by the Comparison Test, the series converges.

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.) 1. For all n > 1, く 3-n n2 5, and the series E converges, so by the Comparison Test, the series E converges. 3-n In(n) In(n) 2. For all n > 1, く is , and the series converges, so by the Comparison Test, the series converges. n2 In(n) converges. In(n) 3. For all n > 2, and the series E converges, so by the Comparison Test, the series E n 1 4. For all n > 1, , and the series 2 E diverges, so by the Comparison Test, the series E diverges. n In(n) In(n) 5. For all n > 2, n In(n) In(n) diverges. , and the series E diverges, so by the Comparison Test, the series n 6. For all n > 2, - n2-6 , and the seriesE converges, so by the Comparison Test, the series converges. A V
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.) 1. For all n > 1, く 3-n n2 5, and the series E converges, so by the Comparison Test, the series E converges. 3-n In(n) In(n) 2. For all n > 1, く is , and the series converges, so by the Comparison Test, the series converges. n2 In(n) converges. In(n) 3. For all n > 2, and the series E converges, so by the Comparison Test, the series E n 1 4. For all n > 1, , and the series 2 E diverges, so by the Comparison Test, the series E diverges. n In(n) In(n) 5. For all n > 2, n In(n) In(n) diverges. , and the series E diverges, so by the Comparison Test, the series n 6. For all n > 2, - n2-6 , and the seriesE converges, so by the Comparison Test, the series converges. A V
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