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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 > 2, <, and the series 2 z converges, so by the Comparison Test, the series 4 converges. 2. For all n > 2, 25 <, and the series E converges, so by the Comparison n²–5 1 Test, the seriesE converges. n²-5 In(n) 3. For all n > 1, n2 < ni5, and the series Ei5 converges, so by the Comparison Test, the series£ converges. In(n) n2 1 4. For all n > 1, <, and the series E converges, so by the Comparison 5-n3 Test, the series E converges. 5-n³ 5. For all n > 1, arctan(n) n3 and the series :£ converges, so by the 2n3 arctan(n) n3 Comparison Test, the series converges. 1 6. For all n > 1, and the series 2E÷ diverges, so by the Comparison n In(n) Test, the series > diverges. n 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 I.) 1. For all n > 2, <, and the series 2 z converges, so by the Comparison Test, the series 4 converges. 2. For all n > 2, 25 <, and the series E converges, so by the Comparison n²–5 1 Test, the seriesE converges. n²-5 In(n) 3. For all n > 1, n2 < ni5, and the series Ei5 converges, so by the Comparison Test, the series£ converges. In(n) n2 1 4. For all n > 1, <, and the series E converges, so by the Comparison 5-n3 Test, the series E converges. 5-n³ 5. For all n > 1, arctan(n) n3 and the series :£ converges, so by the 2n3 arctan(n) n3 Comparison Test, the series converges. 1 6. For all n > 1, and the series 2E÷ diverges, so by the Comparison n In(n) Test, the series > diverges. n 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.) 1 1. For all n > 2, A < 2, and the series 2 converges, so by the Comparison n3–4 Test, the series > n n3-4 converges. 1 2. For all n > 2, 5 1 and the series > n? converges, so by the Comparison n2 , 1 n2-5 converges. In(n) Test, the series > 3. For all n > 1, n2 1 n1.5 and the series > n1.5 1 converges, so by the Comparison C Test, the series > In(n) n2 converges. 1 n2 , 4. For all n > I, 5-n3 and the series E, converges, so by the Comparison 1 n2 Test, the series > n 5-n³ converges. arctan(n) n3 5. For all n > 1, and the series 7) n3 1 converges, so by the 2n3 2 Comparison Test, the series arctan(n) n3 converges. 1 6. For all n > 1, n In(n) < 2, and the series 2 diverges, so by the Comparison n Test, the series E 1 diverges. n In(n)
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 1. For all n > 2, A < 2, and the series 2 converges, so by the Comparison n3–4 Test, the series > n n3-4 converges. 1 2. For all n > 2, 5 1 and the series > n? converges, so by the Comparison n2 , 1 n2-5 converges. In(n) Test, the series > 3. For all n > 1, n2 1 n1.5 and the series > n1.5 1 converges, so by the Comparison C Test, the series > In(n) n2 converges. 1 n2 , 4. For all n > I, 5-n3 and the series E, converges, so by the Comparison 1 n2 Test, the series > n 5-n³ converges. arctan(n) n3 5. For all n > 1, and the series 7) n3 1 converges, so by the 2n3 2 Comparison Test, the series arctan(n) n3 converges. 1 6. For all n > 1, n In(n) < 2, and the series 2 diverges, so by the Comparison n Test, the series E 1 diverges. n In(n)
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