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cos(n) /n Зп + 6 0 cos? (n) /n NA 1. CONV 2. n3 0 8n° – nº + 3/n 3. CONV 8n8 -n³ + 4 00 3n3 DIV 4. nº + 6 00 3n3 CONV 5. nº + 6

cos(n) /n Зп + 6 0 cos? (n) /n NA 1. CONV 2. n3 0 8n° – nº + 3/n 3. CONV 8n8 -n³ + 4 00 3n3 DIV 4. nº + 6 00 3n3 CONV 5. nº + 6

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 1.) In(n) 1. For all n > 2, and the series - converges, so by the Comparison Test, the series E In(n) converges. arctan(n) I, and the series E converges, so by the 2n 2. For all n > 1, arctan(n) Comparison Test, the series E converges. 1. 3. For all n > 1, < 2, and the series 2E diverges, so by the n In(n) Comparison Test, the series diverges. п In(n) In(n) >1, and the series E diverges, so by the Comparison 4. For all n > 2, Test, the series E In(n) diverges. 5. For all n > 2, and the series > converges, so by the Comparison Test, the series E n2-4 n2 4 1 converges. 6. For all n > 2, n 5 2 and the series 2E converges, so by the Comparison Test, the series > n3 5 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 1.) In(n) 1. For all n > 2, and the series - converges, so by the Comparison Test, the series E In(n) converges. arctan(n) I, and the series E converges, so by the 2n 2. For all n > 1, arctan(n) Comparison Test, the series E converges. 1. 3. For all n > 1, < 2, and the series 2E diverges, so by the n In(n) Comparison Test, the series diverges. п In(n) In(n) >1, and the series E diverges, so by the Comparison 4. For all n > 2, Test, the series E In(n) diverges. 5. For all n > 2, and the series > converges, so by the Comparison Test, the series E n2-4 n2 4 1 converges. 6. For all n > 2, n 5 2 and the series 2E converges, so by the Comparison Test, the series > n3 5 converges.
Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.) cos(n) /n NA Зп + 6 * cos (n) /n 2. CONV n3 00 8n° n* + 3/n CONV 3. 8n8 – n3 +4 00 3n3 DIV 4. nº + 6 00 3n3 CONV 5. n4 + 6 n=1
Transcribed Image Text:Test each of the following series for convergence by either the Comparison Test or the Limit Comparison Test. If at least one test can be applied to the series, enter CONV if it converges or DIV if it diverges. If neither test can be applied to the series, enter NA. (Note: this means that even if you know a given series converges by some other test, but the comparison tests cannot be applied to it, then you must enter NA rather than CONV.) cos(n) /n NA Зп + 6 * cos (n) /n 2. CONV n3 00 8n° n* + 3/n CONV 3. 8n8 – n3 +4 00 3n3 DIV 4. nº + 6 00 3n3 CONV 5. n4 + 6 n=1
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