Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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 In(n) 1. For all n > 1, n2 i5, and the series 2 converges, so by the Comparison Test, the series 2 converges. n2 n15 n1.5 1 2. For all n > 2, n2 -6 and the series 24 converges, so by the Comparison Test, the series 1 n2 converges. n2 n2-6 In(n) 3. For all n > 2, n2 In(n) , and the series converges, so by the Comparison Test, the series E converges. n? n2 n2 1 4. For all n > 1, 2, and the series 2 E diverges, so by the Comparison Test, the series > n In(n) diverges. n In(n) n 2 5. For all n > 2, n3-3 and the series 2 converges, so by the Comparison Test, the series 2", converges. n2 n2 n3 –3 arctan(n) arctan(n) 6. For all n > 1 and the series 2+ converges, so by the Comparison Test, the series 2 n3 converges. n3 2n3 n3

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 In(n) 1. For all n > 1, n2 i5, and the series 2 converges, so by the Comparison Test, the series 2 converges. n2 n15 n1.5 1 2. For all n > 2, n2 -6 and the series 24 converges, so by the Comparison Test, the series 1 n2 converges. n2 n2-6 In(n) 3. For all n > 2, n2 In(n) , and the series converges, so by the Comparison Test, the series E converges. n? n2 n2 1 4. For all n > 1, 2, and the series 2 E diverges, so by the Comparison Test, the series > n In(n) diverges. n In(n) n 2 5. For all n > 2, n3-3 and the series 2 converges, so by the Comparison Test, the series 2", converges. n2 n2 n3 –3 arctan(n) arctan(n) 6. For all n > 1 and the series 2+ converges, so by the Comparison Test, the series 2 n3 converges. n3 2n3 n3

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
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.) In(n) 1. For all n > 1, n2 In(n) converges. 1 1 and the series converges, so by the Comparison Test, the series 2 n1.5 n1.5 n2 1 and the series 2 n2 1 converges. 1 2. For all n > 2, n² –6 In(n) 3. For all n > 2, n2 1 n2 converges, so by the Comparison Test, the series 2 n2 -6 In(n) converges. 1 and the series2 converges, so by the Comparison Test, the series 2 n2 n2 1 4. For all n > 1, and the series 22; diverges, so by the Comparison Test, the series 2 1 diverges. n In(n) n In(n) n 5. For all n> 2, 2 and the series 2 2 + n2 n converges, so by the Comparison Test, the series 2". converges. п3 —3 n2 п3 —3 arctan(n) arctan(n) 6. For all n > 1, and the series 2 2n3 converges, so by the Comparison Test, the series 2 n3 converges. n3 n³
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.) In(n) 1. For all n > 1, n2 In(n) converges. 1 1 and the series converges, so by the Comparison Test, the series 2 n1.5 n1.5 n2 1 and the series 2 n2 1 converges. 1 2. For all n > 2, n² –6 In(n) 3. For all n > 2, n2 1 n2 converges, so by the Comparison Test, the series 2 n2 -6 In(n) converges. 1 and the series2 converges, so by the Comparison Test, the series 2 n2 n2 1 4. For all n > 1, and the series 22; diverges, so by the Comparison Test, the series 2 1 diverges. n In(n) n In(n) n 5. For all n> 2, 2 and the series 2 2 + n2 n converges, so by the Comparison Test, the series 2". converges. п3 —3 n2 п3 —3 arctan(n) arctan(n) 6. For all n > 1, and the series 2 2n3 converges, so by the Comparison Test, the series 2 n3 converges. n3 n³
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS