How do we know that Integral test can be applied in testing infinite series whether converges or diverges

Calculus 3

Passage
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Mathematics
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University
•
Easy
Roy Endrano
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36 questions
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1.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the usual behavior of a harmonic series
3.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
What is the alternating series test used for?
To test the convergence or divergence of an infinite series with alternating signs
To test the convergence or divergence of an infinite series with only positive terms
To test the convergence or divergence of an infinite series with only negative terms
To test the convergence or divergence of an infinite series with random terms
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When can the ratio test be applied to determine the convergence of an infinite series?
When the series has alternating signs
When the series has only positive terms
When the series has only negative terms
When the series has terms that are eventually nonzero and follow a certain pattern
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of the root test in analyzing infinite series?
To determine if the series converges absolutely or conditionally
To determine if the series has a finite number of terms
To determine if the series has an infinite number of terms
To determine if the series has a constant ratio between consecutive terms
6.
MULTIPLE CHOICE QUESTION
2 mins • 2 pts
diverging
diverge conditionally
converge conditionally
converging
7.
MULTIPLE CHOICE QUESTION
2 mins • 2 pts
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