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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 1.) 1. For all n > 2, ¹n(n)>, and the series converges, so by the Comparison Test, the series ( > converges. 2. For all n> 1,6n³ converges. In(n) 12 3. For all n > 2, and the series 4. For all n > 2,<, and the series 2Σ converges. 5. For all n > 1, nln(n) 2,¹ <2, and the series converges. and the series converges, so by the Comparison Test, the series 72 diverges, so by the Comparison Test, the series > converges, so by the Comparison Test, the series > n diverges. diverges, so by the Comparison Test, the series ΣmIn(n) converges, so by the Comparison Test, the series Σ²²8

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 1.) 1. For all n > 2, ¹n(n)>, and the series converges, so by the Comparison Test, the series ( > converges. 2. For all n> 1,6n³ converges. In(n) 12 3. For all n > 2, and the series 4. For all n > 2,<, and the series 2Σ converges. 5. For all n > 1, nln(n) 2,¹ <2, and the series converges. and the series converges, so by the Comparison Test, the series 72 diverges, so by the Comparison Test, the series > converges, so by the Comparison Test, the series > n diverges. diverges, so by the Comparison Test, the series ΣmIn(n) converges, so by the Comparison Test, the series Σ²²8

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 > 2, ¹n(n)>, and the series converges, so by the Comparison Test, the series > converges. 2. For all n > 1, converges. 3. For all n > 2, n 6-n³ In(n) n 72 1 7 and the series 4. For all n > 2,<2, converges, so by the Comparison Test, the series > converges. 1 5. For all n > 1, nln(n) < 2/2, and the series 2 Σ diverges. 6. For all n > 2,²8 <2, and the series Σ converges. 72 6-n³ and the series and the series 2Σ converges, so by the Comparison Test, the series Σ - 72 diverges, so by the Comparison Test, the series ΣIn(n) converges, so by the Comparison Test, the series Σ7²-8 In(n) diverges, so by the Comparison Test, the series > diverges.
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 > 2, ¹n(n)>, and the series converges, so by the Comparison Test, the series > converges. 2. For all n > 1, converges. 3. For all n > 2, n 6-n³ In(n) n 72 1 7 and the series 4. For all n > 2,<2, converges, so by the Comparison Test, the series > converges. 1 5. For all n > 1, nln(n) < 2/2, and the series 2 Σ diverges. 6. For all n > 2,²8 <2, and the series Σ converges. 72 6-n³ and the series and the series 2Σ converges, so by the Comparison Test, the series Σ - 72 diverges, so by the Comparison Test, the series ΣIn(n) converges, so by the Comparison Test, the series Σ7²-8 In(n) diverges, so by the Comparison Test, the series > diverges.
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