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Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) 8 2n³ +5 4n³ - 1 (c) n=1 8 (b) Σ n=1 n=1 n²3n (n + 4)n! n=1 3n²-4 cos n 4n4+1 (d) (-1)"+¹n² (−1)n+1,2 3n³ - 2

Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) 8 2n³ +5 4n³ - 1 (c) n=1 8 (b) Σ n=1 n=1 n²3n (n + 4)n! n=1 3n²-4 cos n 4n4+1 (d) (-1)"+¹n² (−1)n+1,2 3n³ - 2

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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Strategy D13 To determine whether a series an is convergent or divergent, do the following. 1. If you think that the sequence of terms (an) is non-null, then try the Non-null Test. 2. If an has non-negative terms, then try one of these tests. Basic series Is an a basic series, or a combination of these? Comparison Test Is an ≤ bn, where bn is convergent, or an ≥ bn ≥ 0, where bn is divergent? Limit Comparison Test Does an behave like bn for large n (that is, does an/bnL0), where bn is a series that you know converges or diverges? Ratio Test Does an+1/an → 1 1? 3. If an has infinitely many positive and negative terms, then try one of these tests. Rom Absolute Convergence Test Is an convergent? (Use step 2.) Alternating Test Is an = (-1)+1bn, where (bn) is non-negative, null and decreasing?
Transcribed Image Text:Strategy D13 To determine whether a series an is convergent or divergent, do the following. 1. If you think that the sequence of terms (an) is non-null, then try the Non-null Test. 2. If an has non-negative terms, then try one of these tests. Basic series Is an a basic series, or a combination of these? Comparison Test Is an ≤ bn, where bn is convergent, or an ≥ bn ≥ 0, where bn is divergent? Limit Comparison Test Does an behave like bn for large n (that is, does an/bnL0), where bn is a series that you know converges or diverges? Ratio Test Does an+1/an → 1 1? 3. If an has infinitely many positive and negative terms, then try one of these tests. Rom Absolute Convergence Test Is an convergent? (Use step 2.) Alternating Test Is an = (-1)+1bn, where (bn) is non-negative, null and decreasing?
Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) (b) Σ n=1 (c) n=1 (d) 8 n=1 2n³ +5 3 4n³ - 1 n²3n (n + 4)n! 3n² - 4 cos n 4n4 +1 (−1)¹+¹n² 3n³ - 2 24 n=1
Transcribed Image Text:Use Strategy D13 from Unit D3 to determine whether each of the following series converges. Name any results or rules that you use. You may use the basic series listed in Theorem D33 from Unit D3. (a) (b) Σ n=1 (c) n=1 (d) 8 n=1 2n³ +5 3 4n³ - 1 n²3n (n + 4)n! 3n² - 4 cos n 4n4 +1 (−1)¹+¹n² 3n³ - 2 24 n=1
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