At least one of the answers above is NOT correct. 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. For all n> 1, 2 <15 and the series Es converges, so by the Comparison Test, the series E In(n) converges. n2 2. For all n > 2, <5, and the series E converges, by the Comparison Test, the series E converges. 3. For all n > 1, and the series - converges, so by the Comparison Test, the series 5 n3 converges. 4. For all n> 1, < 2, and the series 2 diverges, so by the Comparison Test, the series diverges. n In(n) In(n) 5. For all n >: n In(n) , and the series E: diverges, so by the Comparison Test, the series E In(n) diverges. C 6. For all n > 2, . < and the series 2 E converges, so by the Comparison Test, the series E, converges. v v
At least one of the answers above is NOT correct. 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. For all n> 1, 2 <15 and the series Es converges, so by the Comparison Test, the series E In(n) converges. n2 2. For all n > 2, <5, and the series E converges, by the Comparison Test, the series E converges. 3. For all n > 1, and the series - converges, so by the Comparison Test, the series 5 n3 converges. 4. For all n> 1, < 2, and the series 2 diverges, so by the Comparison Test, the series diverges. n In(n) In(n) 5. For all n >: n In(n) , and the series E: diverges, so by the Comparison Test, the series E In(n) diverges. C 6. For all n > 2, . < and the series 2 E converges, so by the Comparison Test, the series E, converges. v v
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I need help with the following questions, please help
Transcribed Image Text:At least one of the answers above is NOT correct.
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. For all n >1
72 <
and the series E converges, so by the Comparison Test, the series >
In(n)
converges.
2. For all n > 2, <.
and the series £ converges, so by the Comparison Test, the series E, converges.
3. For all n > 1, ".
and the series converges, so by the Comparison Test, the series E
5 n3 < 2
<2, and the series 2 diverges, so by the Comparison Test, the series >
5-73 converges.
4. For all n > 1, –
diverges.
n In(n)
In(n)
>, and the series E diverges, so by the Comparison Test, the series E
n In(n)
In(n)
diverges.
5. For all n > 2.
C
6. For all n > 2, 4. <
3, and the series 2 converges, so by the Comparison Test, the series , converges.
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