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) n² 4. For all n > e, 1. For all ne, 2. For all n > 2,23 1, <, and the series n³ > and the series . In(n) > ¹, and the series n n In(n) converges. n² converges, so by the Comparison Test, the series > converges, so by the Comparison Test, the series n²-3 23 converges. converges, so by the Comparison Test, the series > converges. arctan(n) n³ In(n) n diverges, so by the Comparison Test, the series > diverges.
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) n² 4. For all n > e, 1. For all ne, 2. For all n > 2,23 1, <, and the series n³ > and the series . In(n) > ¹, and the series n n In(n) converges. n² converges, so by the Comparison Test, the series > converges, so by the Comparison Test, the series n²-3 23 converges. converges, so by the Comparison Test, the series > converges. arctan(n) n³ In(n) n diverges, so by the Comparison Test, the series > diverges.
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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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 > e,
2. For all n > 2,
3. For all n > 1,
4. For all n > e,
In(n)
n²
1
n²-3
arctan(n)
n³
In(n)
n
<
1
n²
n²
3
and the series Σ
In(n)
n²
n²
1
n²
converges, so by the Comparison Test, the series > converges.
converges, so by the Comparison Test, the series Σ23 converges.
n²-3
, Ξ Σ ;
and the series
1
n3
converges, so by the Comparison Test, the series >
arctan(n)
n³
In(n)
n
and the series Σ
"
T
ग
2n3
1
, and the series Σ diverges, so by the Comparison Test, the series Σ diverges.
n
n
converges.
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