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1. For all n > 2,¹ <, and the series 2. For all n > 1, <, and the series 3. For all n > e, 4. For all n > e, arctan(n) n³ In(n) n In(n) >, and the series n >, and the series n²- converges, so by the Comparison Test, the series converges. arctan(n) converges, so by the Comparison Test, the series > diverges, so by the Comparison Test, the series n³ In(n) diverges. n converges, so by the Comparison Test, the series In(n) converges. converges.

1. For all n > 2,¹ <, and the series 2. For all n > 1, <, and the series 3. For all n > e, 4. For all n > e, arctan(n) n³ In(n) n In(n) >, and the series n >, and the series n²- converges, so by the Comparison Test, the series converges. arctan(n) converges, so by the Comparison Test, the series > diverges, so by the Comparison Test, the series n³ In(n) diverges. n converges, so by the Comparison Test, the series In(n) converges. 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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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.) 1. For all n > 2,2 < 2. For all n > 1, 3. For all n > e, 4. For all n > e, arctan(n) n³ In(n) n In(n) n² and the series n² < and the series Ξ Σ π 2n³ and the series " n² n 1 n² 3 " and the series 1 n converges, so by the Comparison Test, the series 1 2 n³ converges, so by the Comparison Test, the series > In(n) diverges, so by the Comparison Test, the series > diverges. n converges, so by the Comparison Test, the series > Σ n²_ n² converges. arctan(n) n.³ In(n) n² converges. 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.) 1. For all n > 2,2 < 2. For all n > 1, 3. For all n > e, 4. For all n > e, arctan(n) n³ In(n) n In(n) n² and the series n² < and the series Ξ Σ π 2n³ and the series " n² n 1 n² 3 " and the series 1 n converges, so by the Comparison Test, the series 1 2 n³ converges, so by the Comparison Test, the series > In(n) diverges, so by the Comparison Test, the series > diverges. n converges, so by the Comparison Test, the series > Σ n²_ n² converges. arctan(n) n.³ In(n) n² converges. converges.
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