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

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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answer e,f and h only

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