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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 converges, so by the Comparison Test, the series , converges. く 2. For all n > 2, <, and the series converges, so by the Comparison Test, the series E, converges. n2-5 In(n) 3. For all n > 1, < i5, and the series Eis converges, so by the Comparison Test, the series E n In(n) converges. 4. For all n > 1, く 2, and the series E converges, so by the Comparison Test, the series E 5-n converges. 5-n arctan(n) 5. For all n > 1, < , and the series E converges, so by the Comparison Test, the series E arctan(n) converges. 1 6. For all n >1, and the series 2E÷ diverges, so by the Comparison Test, the series E 1 diverges. n In(n) 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 converges, so by the Comparison Test, the series , converges. く 2. For all n > 2, <, and the series converges, so by the Comparison Test, the series E, converges. n2-5 In(n) 3. For all n > 1, < i5, and the series Eis converges, so by the Comparison Test, the series E n In(n) converges. 4. For all n > 1, く 2, and the series E converges, so by the Comparison Test, the series E 5-n converges. 5-n arctan(n) 5. For all n > 1, < , and the series E converges, so by the Comparison Test, the series E arctan(n) converges. 1 6. For all n >1, and the series 2E÷ diverges, so by the Comparison Test, the series E 1 diverges. n In(n) n In(n)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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.) 2 1 1. For all n > 2, and the series 2E n n? converges, so by the Comparison Test, the series > n³–4 converges. n3-4 n2 1 2. For all n > 2, n²-5 1 1 n²–5 converges. In(n) n2 1 and the seriesEz converges, so by the Comparison Test, the series n2 n2 In(n) 3. For all n > 1, n2 < „l5 , and the series „i5 converges, so by the Comparison Test, the series ) n1.5 converges. 4. For all n> 1, 1 n n 5-n3 n2 , and the series z converges, so by the Comparison Test, the series 5-n3 converges. arctan(n) n3 arctan(n) n3 1 5. For all n > 1, 2n3 , and the series 2 converges, so by the Comparison Test, the series converges. n3 1 6. For all n > 1, 2 and the series 2) diverges, so by the Comparison Test, the series 1 n In(n) n In(n) 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.) 2 1 1. For all n > 2, and the series 2E n n? converges, so by the Comparison Test, the series > n³–4 converges. n3-4 n2 1 2. For all n > 2, n²-5 1 1 n²–5 converges. In(n) n2 1 and the seriesEz converges, so by the Comparison Test, the series n2 n2 In(n) 3. For all n > 1, n2 < „l5 , and the series „i5 converges, so by the Comparison Test, the series ) n1.5 converges. 4. For all n> 1, 1 n n 5-n3 n2 , and the series z converges, so by the Comparison Test, the series 5-n3 converges. arctan(n) n3 arctan(n) n3 1 5. For all n > 1, 2n3 , and the series 2 converges, so by the Comparison Test, the series converges. n3 1 6. For all n > 1, 2 and the series 2) diverges, so by the Comparison Test, the series 1 n In(n) n In(n) diverges.
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