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In(n) In(n) 1. For all n > 2, n2 and the series converges, so by the Comparison Test, the series E n2 n2 n2 converges. In(n) In(n) 2. For all n > 1, n2 and the series converges, so by the Comparison Test, the series n1.5 : n1.5 n2 converges. 3. For all n > 2, , < and the series converges, so by the Comparison Test, the series n2-4 n2' n2-4 converges.

In(n) In(n) 1. For all n > 2, n2 and the series converges, so by the Comparison Test, the series E n2 n2 n2 converges. In(n) In(n) 2. For all n > 1, n2 and the series converges, so by the Comparison Test, the series n1.5 : n1.5 n2 converges. 3. For all n > 2, , < and the series converges, so by the Comparison Test, the series n2-4 n2' n2-4 converges.

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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9. 1,2,3

) 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.) In(n) > 1 and the series ) n2 converges, so by the Comparison Test, the series > n2 In(n) 1. For all n > 2, n2 n2' converges. In(n) 2. For all n > 1, n2 In(n) 1 1 and the series ) n1.5 converges, so by the Comparison Test, the series ) n2 n1.5 : converges. 3. For all n > 2, 1 n2 and the series>) n2 converges, so by the Comparison Test, the series > n2-4 n2-4 converges. arctan(n) 4. For all n > 1, and the series 2 n3 converges, so by the Comparison Test, the series n3 2n3 arctan(n) converges. n3 In(n) 5. For all n > 2, 1 and the series E diverges, so by the Comparison Test, the series In(n) diverges. n n n 6. For all n >1, and the series 2 diverges, so by the Comparison Test, the series 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.) In(n) > 1 and the series ) n2 converges, so by the Comparison Test, the series > n2 In(n) 1. For all n > 2, n2 n2' converges. In(n) 2. For all n > 1, n2 In(n) 1 1 and the series ) n1.5 converges, so by the Comparison Test, the series ) n2 n1.5 : converges. 3. For all n > 2, 1 n2 and the series>) n2 converges, so by the Comparison Test, the series > n2-4 n2-4 converges. arctan(n) 4. For all n > 1, and the series 2 n3 converges, so by the Comparison Test, the series n3 2n3 arctan(n) converges. n3 In(n) 5. For all n > 2, 1 and the series E diverges, so by the Comparison Test, the series In(n) diverges. n n n 6. For all n >1, and the series 2 diverges, so by the Comparison Test, the series n In(n) n In(n) diverges.
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