1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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Question
1
(a) Use the Integral Test to show that >,
converges.
2
d
1
n' +1
n = 0
-1
Hint:
tan
dx
X =
1+x?
3/2
n
(b) Use a Comparison Test to show that >
diverges.
+ 14
2
n =1
(c) Use the Ratio Test theorem to determine whether the series
2"
Σ
(n+1)
is convergent or divergent.
n = 1
(d) The alternating series 2Y
(-1)**1
is conditionally
n = 1
n
convergent.
Justify this statement.
Transcribed Image Text:1 (a) Use the Integral Test to show that >, converges. 2 d 1 n' +1 n = 0 -1 Hint: tan dx X = 1+x? 3/2 n (b) Use a Comparison Test to show that > diverges. + 14 2 n =1 (c) Use the Ratio Test theorem to determine whether the series 2" Σ (n+1) is convergent or divergent. n = 1 (d) The alternating series 2Y (-1)**1 is conditionally n = 1 n convergent. Justify this statement.
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