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For each of the following series determine if they converge or diverge. You may use any test we have -covered so far. (2) Σ n=1 3+ cos(n!) 玩 (b) Σn2 sin(n3/2) n=1 ∞ (3n)! (c) (-1) (n!)362n+1 n=1

For each of the following series determine if they converge or diverge. You may use any test we have -covered so far. (2) Σ n=1 3+ cos(n!) 玩 (b) Σn2 sin(n3/2) n=1 ∞ (3n)! (c) (-1) (n!)362n+1 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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Question 2 ( using one of these : nth term test, direct comparison test , limit comparison test , ratio test , integral test or root test ) Question 3
utions to each of these problems on a seperate sheet of paper. 1. Consider the series n=1 In(n) n2 (a) Try using the Limit Comparison Test with b (b) Try using the Limit Comparison Test with b 1 = 1221 1 Is the test conclusive? Explain your answer. Ba =. Is the test conclusive? Explain your answer. (c) Try using the Limit Comparison Test with b n 1 = n3/2- Is the test conclusive? Explain your answer. 2. For each of the following series determine if they converge or diverge. You may use any test we have covered so far. (a) 3+ cos(n!) 玩 n=1 (b)²sin*(3/2) n=1 (c) (-1)"; n=1 (3n)! (n!)362n+1 (d) sin (+) (e) (f) n=2 n=3 n=0 √n²-4 m³ +In(n) 2.5...(3n+2) 2nn! (The expression in the numerator is called a running product. It is basically a factorial that skips numbers rather than multiplying every number together. This one starts at 2 and skips by 3 each time. So for instance, if n was 4 it would be 2.5.8.11.14.) 3. Let an and bn be two sequences of positive numbers such that bn diverges. (a) If lim An+1 (b) If lim An (c) If lim an n7x (d) If lim va 8012 = = 1 1 2' ེ 2' = 1 1 2' does an converge or diverge and what test justifies your conclusion? does an converge or diverge and what test justifies your conclusion? does an converge or diverge and what test justifies your conclusion? 2' does an converge or diverge and what test justifies your conclusion?
Transcribed Image Text:utions to each of these problems on a seperate sheet of paper. 1. Consider the series n=1 In(n) n2 (a) Try using the Limit Comparison Test with b (b) Try using the Limit Comparison Test with b 1 = 1221 1 Is the test conclusive? Explain your answer. Ba =. Is the test conclusive? Explain your answer. (c) Try using the Limit Comparison Test with b n 1 = n3/2- Is the test conclusive? Explain your answer. 2. For each of the following series determine if they converge or diverge. You may use any test we have covered so far. (a) 3+ cos(n!) 玩 n=1 (b)²sin*(3/2) n=1 (c) (-1)"; n=1 (3n)! (n!)362n+1 (d) sin (+) (e) (f) n=2 n=3 n=0 √n²-4 m³ +In(n) 2.5...(3n+2) 2nn! (The expression in the numerator is called a running product. It is basically a factorial that skips numbers rather than multiplying every number together. This one starts at 2 and skips by 3 each time. So for instance, if n was 4 it would be 2.5.8.11.14.) 3. Let an and bn be two sequences of positive numbers such that bn diverges. (a) If lim An+1 (b) If lim An (c) If lim an n7x (d) If lim va 8012 = = 1 1 2' ེ 2' = 1 1 2' does an converge or diverge and what test justifies your conclusion? does an converge or diverge and what test justifies your conclusion? does an converge or diverge and what test justifies your conclusion? 2' does an converge or diverge and what test justifies your conclusion?
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