arctan(n) T 4. For all n ≥ 2, n³ 3 2n³ converges, so by the Comparison Test, the series > ? ? 5. For all n ≥ 3, the Comparison Test, the series ? 6. For all n ≥ 3, Comparison Test, the series > In(n) 1 n² n² In(n) n² In(n) n In(n) n " > and the series arctan(n) n³ converges. converges. and the series Σ " n² 1 , and the series diverges, so by the n diverges. - converges, so by n

arctan(n) T 4. For all n ≥ 2, n³ 3 2n³ converges, so by the Comparison Test, the series > ? ? 5. For all n ≥ 3, the Comparison Test, the series ? 6. For all n ≥ 3, Comparison Test, the series > In(n) 1 n² n² In(n) n² In(n) n In(n) n " > and the series arctan(n) n³ converges. converges. and the series Σ " n² 1 , and the series diverges, so by the n diverges. - converges, so by n

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 68E

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Question

Below are statements to show if a series is convergent or divergent only using the comparison test. Determine whether each statement is correct or incorrect:

arctan(n) T
4. For all n ≥ 2,
n³
3
2n³
converges, so by the Comparison Test, the series >
?
?
5. For all n ≥ 3,
the Comparison Test, the series
?
6. For all n ≥ 3,
Comparison Test, the series
In(n) 1
n²
n²
In(n)
n²
In(n)
n
In(n)
n
"
>
and the series
arctan(n)
n³
converges.
converges.
and the series Σ
"
n²
1
, and the series diverges, so by the
n
diverges.
1
-
converges, so by
n

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