
Understanding the Ratio Test for Series Convergence

Interactive Video
•
Mathematics, Science
•
9th - 12th Grade
•
Hard

Ethan Morris
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary purpose of using the ratio test in series analysis?
To calculate the derivative of the series
To determine if the series converges or diverges
To find the sum of the series
To find the integral of the series
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the ratio test, what does it mean if the limit L is less than one?
The series diverges
The series converges
The test is inconclusive
The series oscillates
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the ratio test particularly useful for series involving exponentials or factorials?
Because it simplifies the calculation of the series sum
Because it is the only test applicable to such series
Because it handles the growth rates of exponentials and factorials effectively
Because it provides a quick approximation of the series
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the expression for a(n+1) in the given example?
3^n / n!
3^(n+1) / (n+1)!
n! / 3^n
3^n / (n+1)!
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When simplifying the ratio of a(n+1) to a(n), what happens to the base 3 terms?
They double in the numerator
They remain unchanged
They simplify to one factor of 3
They cancel out completely
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do the factorial terms simplify in the ratio test example?
They cancel out completely
They simplify to one factor of n+1 in the denominator
They double in the numerator
They remain unchanged
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final simplified limit in the example?
Infinity
0
1
3
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