
Understanding Series Convergence and Divergence

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Mia Campbell
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in determining if an infinite series converges or diverges?
Calculate the sum of the series.
Use the ratio test.
Apply the nth term Divergent test.
Check if the series is geometric.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the nth term Divergent test conclude if the limit of a_n as n approaches infinity is not zero?
The series is alternating.
The series converges.
The test is inconclusive.
The series diverges.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the nth term Divergent test inconclusive when the limit of a_n is zero?
Because it doesn't determine convergence.
Because the series is finite.
Because the series is geometric.
Because the series is alternating.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main condition for the Alternating Series Test to conclude convergence?
The terms must increase in absolute value.
The series must be finite.
The terms must decrease in absolute value.
The series must be geometric.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the Alternating Series Test, what must be true about a_n and a_(n+1)?
a_n must equal a_(n+1).
a_n must be less than a_(n+1).
a_n must be zero.
a_n must be greater than a_(n+1).
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What conclusion is reached after applying the Alternating Series Test to the given series?
The series is geometric.
The series converges.
The series diverges.
The series is inconclusive.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What additional check is necessary for alternating series after determining convergence?
Check for absolute convergence.
Check for geometric properties.
Check for increasing terms.
Check for finite terms.
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