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Calculus: Limit Comparison 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 Limit Comparison Test to rational and polynomial series. Includes examples where the test shows convergence, divergence, and inconclusive cases. Perfect for strengthening problem‑solving skills and mastering exam‑style questions.

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Practice Problems: Limit Comparison Test



Practice Questions
P n2 +1
1. Test convergence of n3 +5
.
P 2n3 +1
2. Apply the Limit Comparison Test to n4
.
P n2
3. Determine convergence of n3 +10
.
P n3 +4 P 1
4. Compare n5
with n2
.
P n2 −3
5. Use the Limit Comparison Test on n4 +2
.
n3
P
6. Analyze n3 +1
.
n2 +5
P
7. Test convergence of n2 +10n
.
n4
P
8. Apply the Limit Comparison Test to n5 +2
.
n2
P
9. Determine convergence of n2 +1
.
P n3 +2 P 1
10. Compare n4 +5
with n
.
n2
P
11. Use the Limit Comparison Test on n3 +2n
.
n5
P
12. Analyze n6 +1
.
P n2 +1
13. Test convergence of n4 +3
.
n3
P
14. Apply the Limit Comparison Test to n4 +n
.
n2
P
15. Determine convergence of n3 +n2
.
n4 1
P P
16. Compare n5 +10
with n
.
n3
P
17. Use the Limit Comparison Test on n5 +2
.
n2
P
18. Analyze n4 +1
.


1

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Browse related subjects

Subjects

  • stepbystep solutions
  • infinite series
  • limit comparison test practice problems
  • convergence and divergence exercises
  • polynomial problem set calculus
  • harmonic series comparison
  • p series practice questions

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