What is the interval of convergence in the context of a power series?

Understanding Interval of Convergence

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

Amelia Wright
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The range of x values for which the series converges
The range of x values for which the series diverges
The range of x values for which the series is undefined
The range of x values for which the series is constant
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which test is initially applied to find the open interval of convergence?
Root Test
Comparison Test
Integral Test
Ratio Test
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the ratio test, what must the limit be for the series to converge?
Equal to 1
Equal to 0
Greater than 1
Less than 1
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified form of the limit in the ratio test for this series?
Absolute value of 2x
Absolute value of 3x
Absolute value of 4x
Absolute value of x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the open interval of convergence found after solving the inequality?
(-1, 1)
(-1/2, 1/2)
(-2, 2)
(-1/3, 1/3)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the series at x = -1/2?
The series is constant
The series converges
The series diverges
The series is undefined
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the nth term divergence test at x = 1/2?
The limit equals zero
The limit is undefined
The limit equals one
The limit is negative
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