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Exam (elaborations)

Calculus: Ratio Test Practice Problems

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2025/2026 Written for academic year
Institution Senior / 12th Grade
Course Calculus
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A set of 20 practice problems with step‑by‑step solutions applying the Ratio Test to factorials, exponentials, geometric series, and p‑series. Includes examples where the test is conclusive and inconclusive, helping students master exam‑style problems. Perfect for strengthening problem‑solving skills.

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Practice Problems: Ratio Test



Practice Questions
1
P
1. Test convergence of n!
.
1 n
P 
2. Apply the Ratio Test to 2
.
P n
3. Determine convergence of 2n
.
P1
4. Use the Ratio Test on n
.
P n2
5. Analyze n!
.
P 3n
6. Test convergence of n!
.
P 1
7. Apply the Ratio Test to n2
.
P n!
8. Determine convergence of nn
.
P 5n
9. Use the Ratio Test on n2
.
Pn
10. Analyze n!
.
P 2n
11. Test convergence of n!
.
P 1
12. Apply the Ratio Test to n3
.
P n3
13. Determine convergence of 3n
.
P n!
14. Use the Ratio Test on 2n
.
P 1
15. Analyze nn
.
P n2
16. Test convergence of 2n
.
P n
17. Apply the Ratio Test to 3n
.
P n!
18. Determine convergence of n3
.
P nn
19. Use the Ratio Test on n!
.
P 1
20. Analyze (n!)2
.


1

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Uploaded on
August 3, 2026
Number of pages
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Written in
2025/2026
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Browse related subjects

Subjects

  • stepbystep solutions
  • infinite series
  • ratio test practice problems
  • convergence and divergence exercises
  • factorial problem set calculus
  • geometric series practice questions
  • harmonic series test problems

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