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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.) с C C C T C 1. For all n > 2,¹ 1,6 3. For all n > 1 < and the series 4. For all n > 1, 5. For all n > 1, arctan(n) n³ n(n) < 15, and the series 72² -- n ln(n) converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series In(n) 6. For all n > 2,>, and the series converges. converges. arctan(n) converges. converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series (n) converges. 2, and the series 2 Σ diverges, so by the Comparison Test, the series ΣIn(n) diverges. converges, so by the Comparison Test, the series converges. In(n)

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.) с C C C T C 1. For all n > 2,¹ 1,6 3. For all n > 1 < and the series 4. For all n > 1, 5. For all n > 1, arctan(n) n³ n(n) < 15, and the series 72² -- n ln(n) converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series In(n) 6. For all n > 2,>, and the series converges. converges. arctan(n) converges. converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series (n) converges. 2, and the series 2 Σ diverges, so by the Comparison Test, the series ΣIn(n) diverges. converges, so by the Comparison Test, the series converges. In(n)

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.) C C C C I C 1. For all n > 2,¹ <2, and the series 2Σ 2. For all n >1 and the series converges, so by the Comparison Test, the series Σ converges. converges, so by the Comparison Test, the series converges. 6-³ arctan(n) arctan(n) converges, so by the Comparison Test, the series > n³ In(n) converges, so by the Comparison Test, the series - 3. For all n > 1, < 23, and the series n³ 4. For all n > 1 15, and the series In(n) 72converges. 5. For all n > 1, nln(n) < 1212, and the series 2 Σ diverges, so by the Comparison Test, the series Σn(n) diverges. converges, so by the Comparison Test, the series Σ In(n) 6. For all n > 2, > 2, and the series In(n) 72² converges. 6-n³ converges.
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.) C C C C I C 1. For all n > 2,¹ <2, and the series 2Σ 2. For all n >1 and the series converges, so by the Comparison Test, the series Σ converges. converges, so by the Comparison Test, the series converges. 6-³ arctan(n) arctan(n) converges, so by the Comparison Test, the series > n³ In(n) converges, so by the Comparison Test, the series - 3. For all n > 1, < 23, and the series n³ 4. For all n > 1 15, and the series In(n) 72converges. 5. For all n > 1, nln(n) < 1212, and the series 2 Σ diverges, so by the Comparison Test, the series Σn(n) diverges. converges, so by the Comparison Test, the series Σ In(n) 6. For all n > 2, > 2, and the series In(n) 72² converges. 6-n³ converges.
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