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8. 8. ト k=0 7. Determine whether the following series converge absolutely, conditionally, or diverge. Provide justification for your conclusions. These may not be exactly the same as what will appear on the exam, but they should give you an idea of what will be asked. (-1)" (2n)! -1)" Vn (a) (c) n=1 n=1 n4 – 4n 3 (4) E(-)* (b) (d) n6 + 9n2 + 3 n=7 n=1

8. 8. ト k=0 7. Determine whether the following series converge absolutely, conditionally, or diverge. Provide justification for your conclusions. These may not be exactly the same as what will appear on the exam, but they should give you an idea of what will be asked. (-1)" (2n)! -1)" Vn (a) (c) n=1 n=1 n4 – 4n 3 (4) E(-)* (b) (d) n6 + 9n2 + 3 n=7 n=1

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
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How would you prove 7(b)?

6. Consider the series ark k=0 (a) Prove that ) ar* diverges whenever r| > 1. k=0 a (b) Prove that ) ark if and only if |r| < 1. 1 - r k=0 7. Determine whether the following series converge absolutely, conditionally, or diverge. Provide justification for your conclusions. These may not be exactly the same as what will appear on the exam, but they should give you an idea of what will be asked. (a) (-1)" (2n)! n (c) (-1)" n=1 n=1 n n1 – 4n (b) Z n6+9n2 + 3 (d)> - n=1 n=7 8. Prove that if ) ak converges, then (ak) → 0. k=1 9. Let l(A) denote the length of A CR. (a) Prove that A C B implies l(A) < e(B), 8. 8.
Transcribed Image Text:6. Consider the series ark k=0 (a) Prove that ) ar* diverges whenever r| > 1. k=0 a (b) Prove that ) ark if and only if |r| < 1. 1 - r k=0 7. Determine whether the following series converge absolutely, conditionally, or diverge. Provide justification for your conclusions. These may not be exactly the same as what will appear on the exam, but they should give you an idea of what will be asked. (a) (-1)" (2n)! n (c) (-1)" n=1 n=1 n n1 – 4n (b) Z n6+9n2 + 3 (d)> - n=1 n=7 8. Prove that if ) ak converges, then (ak) → 0. k=1 9. Let l(A) denote the length of A CR. (a) Prove that A C B implies l(A) < e(B), 8. 8.
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