(-1)"-2 (e) Alternating Series Test: 3" + 3n n=0

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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e only

topic: Sequence and Series

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: D
(e) Alternating Series Test:
n=0
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)
Vn? – n – 1
(c) Root Test:
n=2
n=2
4n cos (nn)
2n2 + 1
(1 – sin (n)) (1+ sin (n))
n2 + 8n + 1
(d) Alternating Series Test:
(h) Comparison Test
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 3" + 3n (a) Ratio Test: D (e) Alternating Series Test: n=0 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) Vn? – n – 1 (c) Root Test: n=2 n=2 4n cos (nn) 2n2 + 1 (1 – sin (n)) (1+ sin (n)) n2 + 8n + 1 (d) Alternating Series Test: (h) Comparison Test n=3 n=1
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