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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.) | 21/12 , and the series 2Σ <2, and the series arctan(n) converges. converges. arctan(n) <2, and the series 12³ 12³ In(n) 72² and the series 1. For all n > 2,8 < 2. For all n > 1,6 3. For all n > 1, < converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series Σ Σ converges, so by the Comparison Test, the series Σ- converges, so by the Comparison Test, the series Σ ¹() 4. For all n > 1, converges. 5. For all n > 1, nln(n) < 1/12, and the series 2 Σ diverges, so by the Comparison Test, the series Σ nin(n) diverges. converges, so by the Comparison Test, the series Σ. In(n) In(n) 6. For all n > 2. and the series 7² converges. 2 converges.

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.) | 21/12 , and the series 2Σ <2, and the series arctan(n) converges. converges. arctan(n) <2, and the series 12³ 12³ In(n) 72² and the series 1. For all n > 2,8 < 2. For all n > 1,6 3. For all n > 1, < converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series Σ Σ converges, so by the Comparison Test, the series Σ- converges, so by the Comparison Test, the series Σ ¹() 4. For all n > 1, converges. 5. For all n > 1, nln(n) < 1/12, and the series 2 Σ diverges, so by the Comparison Test, the series Σ nin(n) diverges. converges, so by the Comparison Test, the series Σ. In(n) In(n) 6. For all n > 2. and the series 7² converges. 2 converges.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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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 > 2,¹ <2, and the series 2Σ converges, so by the Comparison Test, the series 2. For all n > 1,6³ <2, and the series converges, so by the Comparison Test, the series Σ converges, so by the Comparison Test, the series 3. For all n > 1, 27³ and the series 15, and the series converges, so by the Comparison Test, the series and the series 2 Σ diverges, so by the Comparison Test, the series > 2/2 n 4. For all n > 1, 5. For all n > 1, 6. For all n > 2, arctan(n) n2³ In(n) 7² (n) (n)>, and the series converges. converges. arctan(n) converges. n.³ In(n) - converges. 7² diverges. nln(n) In(n) converges, so by the Comparison Test, the series (1) 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 > 2,¹ <2, and the series 2Σ converges, so by the Comparison Test, the series 2. For all n > 1,6³ <2, and the series converges, so by the Comparison Test, the series Σ converges, so by the Comparison Test, the series 3. For all n > 1, 27³ and the series 15, and the series converges, so by the Comparison Test, the series and the series 2 Σ diverges, so by the Comparison Test, the series > 2/2 n 4. For all n > 1, 5. For all n > 1, 6. For all n > 2, arctan(n) n2³ In(n) 7² (n) (n)>, and the series converges. converges. arctan(n) converges. n.³ In(n) - converges. 7² diverges. nln(n) In(n) converges, so by the Comparison Test, the series (1) converges.
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