Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Apply the alternating series test to discuss convergence or divergence of the given series.
Ο
α
Σ(-1)"+1
n=1
O
O
O
h=.
Since
M8
Σ
(-1)
n=1|
Since
Since
1
n=1 n4
α
Σ (-1)
n =]
(-1)'
) "+1
Since
n=1 h
Σ (-1)
n=1
n+1
το
1
n=1 n'
Σ (-1)
n=1
1
n
00 1
n+1
n=1 n'
converges, then the original series is absolutely convergent.
n+1
η
1
· diverges, then the original series is divergent.
1
n²
+1
n
1
Σ which is a convergent p-series.
n=1 n'
00
Σ
n=1 ht
n-
1
2
∞0 1
Σ
n=1 n2
converges, then the original series is conditionally convergent.
Σ
n=1
which is a divergent harmonic series.
1
which is a convergent geometric series.
1
-Σ.
η
n=1 h
diverges, then the original series is divergent.
which is a divergent p-series.
which is a convergent p- series.
00
1
Since Σ converges, then the original series is conditionally convergent.
n=1 n°](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30fc4209-43ac-409b-8363-1a56de792bf2%2F3ba96ccf-1dd8-49c0-9c5d-cdca966ecbd3%2Fc2qay6_processed.png&w=3840&q=75)
Transcribed Image Text:Apply the alternating series test to discuss convergence or divergence of the given series.
Ο
α
Σ(-1)"+1
n=1
O
O
O
h=.
Since
M8
Σ
(-1)
n=1|
Since
Since
1
n=1 n4
α
Σ (-1)
n =]
(-1)'
) "+1
Since
n=1 h
Σ (-1)
n=1
n+1
το
1
n=1 n'
Σ (-1)
n=1
1
n
00 1
n+1
n=1 n'
converges, then the original series is absolutely convergent.
n+1
η
1
· diverges, then the original series is divergent.
1
n²
+1
n
1
Σ which is a convergent p-series.
n=1 n'
00
Σ
n=1 ht
n-
1
2
∞0 1
Σ
n=1 n2
converges, then the original series is conditionally convergent.
Σ
n=1
which is a divergent harmonic series.
1
which is a convergent geometric series.
1
-Σ.
η
n=1 h
diverges, then the original series is divergent.
which is a divergent p-series.
which is a convergent p- series.
00
1
Since Σ converges, then the original series is conditionally convergent.
n=1 n°
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