Answered: converges. 5. For all n > 1, diverges.…

converges. 5. For all n > 1, diverges. n3³-1 1 n ln(n) n² n³-1 2, and the series 2 / diverges, so by the Comparison Test, the series Σ nln(n) n

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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Question

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.)

4. For all n > 2,
n
n³ -1
2
n²
1
I
and the series 2 Σ
converges, so by the Comparison Test, the series >
n
n³_1
converges.
1
5. For all n > 1, (n)</2, and the series 2 Σ diverges, so by the Comparison Test, the series Σ n ln(n)
n
diverges.

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