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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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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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