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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.) converges. In(n) 1. For all n > 1, () <15, and the series Σ converges, so by the Comparison Test, the series Σ converges. n² 2. For all n > 2, In(n) n² 3. For all n > 2, and the series , and the series 28, and the series > 4. For all n > 2, < 5. For all n > 1, nln(n) <2, and the series 2 Σ <2, and the series 6. For all n > 1, arctan(n) n³ In(n) n In(n) n² > In(n) n² converges. n converges, so by the Comparison Test, the series Σ diverges, so by the Comparison Test, the series (n) diverges. converges, so by the Comparison Test, the series Σ converges. diverges, so by the Comparison Test, the series Σnn(n) diverges. converges, so by the Comparison Test, the series - arctan(n) 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.) converges. In(n) 1. For all n > 1, () <15, and the series Σ converges, so by the Comparison Test, the series Σ converges. n² 2. For all n > 2, In(n) n² 3. For all n > 2, and the series , and the series 28, and the series > 4. For all n > 2, < 5. For all n > 1, nln(n) <2, and the series 2 Σ <2, and the series 6. For all n > 1, arctan(n) n³ In(n) n In(n) n² > In(n) n² converges. n converges, so by the Comparison Test, the series Σ diverges, so by the Comparison Test, the series (n) diverges. converges, so by the Comparison Test, the series Σ converges. diverges, so by the Comparison Test, the series Σnn(n) diverges. converges, so by the Comparison Test, the series - arctan(n) 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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17. Practice similar Help me with this 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 flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) argument is converges. - I → ← 1. For all n > 1, 2. For all n > 2, 3. For all n > 2, 4. For all n > 2, 5. For all n > 1, 6. For all n > 1, In(n) n² In(n) n² In(n) n <15, and the series Σ15 converges, so by the Comparison Test, the series Σ n1.5 converges, so by the Comparison Test, the series diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series Σ n²-8 n², and the series >, and the series Σ n ²¹⁄8 <2, and the series n² arctan(n) n³ In(n) n² TT 2n3, Previous Next > In(n) n converges. In(n) (2) converges. diverges. converges. 1 nln(n) </2, and the series 21 diverges, so by the Comparison Test, the series (n) diverges. n and the series converges, so by the Comparison Test, the series > arctan(n) n³
Transcribed Image Text:17. Practice similar Help me with this 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 flawed. (Note: if the conclusion is true but the argument that led to it was wrong, you must enter I.) argument is converges. - I → ← 1. For all n > 1, 2. For all n > 2, 3. For all n > 2, 4. For all n > 2, 5. For all n > 1, 6. For all n > 1, In(n) n² In(n) n² In(n) n <15, and the series Σ15 converges, so by the Comparison Test, the series Σ n1.5 converges, so by the Comparison Test, the series diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series Σ n²-8 n², and the series >, and the series Σ n ²¹⁄8 <2, and the series n² arctan(n) n³ In(n) n² TT 2n3, Previous Next > In(n) n converges. In(n) (2) converges. diverges. converges. 1 nln(n) </2, and the series 21 diverges, so by the Comparison Test, the series (n) diverges. n and the series converges, so by the Comparison Test, the series > arctan(n) n³
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