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In(n) n 3. For all n > 2, 4. For all n > 2,<, 5. For all n > 1, n ln(n) 6. For all n > 2,2²8 >, and the series Σ n and the series 2 , and the series 2 and the series n², 72 diverges, so by the Comparison Test, the series - In(n) converges, so by the Comparison Test, the series conve (n) diverge diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series Σ converge diverges.

In(n) n 3. For all n > 2, 4. For all n > 2,<, 5. For all n > 1, n ln(n) 6. For all n > 2,2²8 >, and the series Σ n and the series 2 , and the series 2 and the series n², 72 diverges, so by the Comparison Test, the series - In(n) converges, so by the Comparison Test, the series conve (n) diverge diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series Σ converge diverges.

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 49E
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Compassion Test Problem 5

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, 2. For all n> 1, 3. For all n > 2, 4. For all n > 2, 5. For all n > 1, 6. For all n > 2, In(n) 6-n' In(n) 3 n³_1 1 n In (n) 1 n²-8 2 n² 22 n and the series Σ and the series and the series and the series 2 Σ and the series 2 and the series - n converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series diverges, so by the Comparison Test, the series > In(n) converges, so by the Comparison Test, the series > n² = diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series n converges. 3 converges. diverges. 6-n³ converges. n³-1 (n) diverges. converges. 1 n²-8
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.) 1. For all n > 2, 2. For all n> 1, 3. For all n > 2, 4. For all n > 2, 5. For all n > 1, 6. For all n > 2, In(n) 6-n' In(n) 3 n³_1 1 n In (n) 1 n²-8 2 n² 22 n and the series Σ and the series and the series and the series 2 Σ and the series 2 and the series - n converges, so by the Comparison Test, the series converges, so by the Comparison Test, the series diverges, so by the Comparison Test, the series > In(n) converges, so by the Comparison Test, the series > n² = diverges, so by the Comparison Test, the series converges, so by the Comparison Test, the series n converges. 3 converges. diverges. 6-n³ converges. n³-1 (n) diverges. converges. 1 n²-8
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