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For each of the following series determine if the series converges or diverges using the indicated test for series convergence or divergence. (-1)"-2 3" + 3n (a) Ratio Test: (n+1)! n=0 (e) Alternating Series Test: n+2 1 (b) Ratio Test: (f) Integral test: 51-n (n + 1) n In n In(ln n) n=3 (g) Comparison Test/Limit Comparison Test: 5n2 – 2n + 1 3n2 + n – 3 V2 + cos² (5n) Vn2 – n – 1 (c) Root Test: n=2 4n cos (na) 2n2 + 1 (1 – sin (n)) (1 + sin (n (d) Alternating Series Test: (h) Comparison Test n2 + 8n + 1 n=3 n=1

For each of the following series determine if the series converges or diverges using the indicated test for series convergence or divergence. (-1)"-2 3" + 3n (a) Ratio Test: (n+1)! n=0 (e) Alternating Series Test: n+2 1 (b) Ratio Test: (f) Integral test: 51-n (n + 1) n In n In(ln n) n=3 (g) Comparison Test/Limit Comparison Test: 5n2 – 2n + 1 3n2 + n – 3 V2 + cos² (5n) Vn2 – n – 1 (c) Root Test: n=2 4n cos (na) 2n2 + 1 (1 – sin (n)) (1 + sin (n (d) Alternating Series Test: (h) Comparison Test n2 + 8n + 1 n=3 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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For each of the following series determine if the series converges or diverges using the indicated test for series convergence or divergence. (-1)"-2 (a) Ratio Test: E n³+n? (n+1)! n=0 (e) Alternating Series Test: 3" + 3n n=0 n+2 1 (b) Ratio Test: (f) Integral test: 51-n (n + 1) n In n In(ln n) n=1 n=3 (g) Comparison Test/Limit Comparison Test: 5n² – 2n + 1' 3n2 + n – 3 /2 + cos² (5n) Vn² – n – 1 (c) Root Test: n=2 (1 – sin (n)) (1 + sin (n n² + 8n +1 4n cos (na) (d) Alternating Series Test: (h) Comparison Test 2n2 + 1 n=3 n=1
Transcribed Image Text:For each of the following series determine if the series converges or diverges using the indicated test for series convergence or divergence. (-1)"-2 (a) Ratio Test: E n³+n? (n+1)! n=0 (e) Alternating Series Test: 3" + 3n n=0 n+2 1 (b) Ratio Test: (f) Integral test: 51-n (n + 1) n In n In(ln n) n=1 n=3 (g) Comparison Test/Limit Comparison Test: 5n² – 2n + 1' 3n2 + n – 3 /2 + cos² (5n) Vn² – n – 1 (c) Root Test: n=2 (1 – sin (n)) (1 + sin (n n² + 8n +1 4n cos (na) (d) Alternating Series Test: (h) Comparison Test 2n2 + 1 n=3 n=1
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