Practice Problems: Absolute vs Conditional
Convergence
Practice Questions
P (−1)n
1. Determine whether n
converges absolutely or conditionally.
P (−1)n
2. Test convergence of n2
.
P (−1)n
3. Does √
n
converge absolutely or conditionally?
P (−1)n
4. Apply the definition of absolute convergence to n3
.
P (−1)n
5. Approximate the sum of the first 5 terms of n
.
P (−1)n
6. Show that n
diverges absolutely.
P (−1)n P1
7. Compare n
with n
.
P (−1)n
8. Determine convergence of n1.5
.
P (−1)n
9. Use the ratio test to analyze n!
.
P (−1)n
10. Prove absolute convergence of n4
.
11. Show conditional convergence of the alternating harmonic series.
P (−1)n
12. Test convergence of n+1
.
P10 (−1)n
13. Approximate n=1 n
.
14. Explain why absolute convergence implies convergence.
15. Compare rearrangements of conditionally convergent series.
P (−1)n
16. Determine whether n1.01
converges absolutely.
P (−1)n
17. Show divergence of 3n .
√
P (−1)n
18. Apply the root test to 2n
.
1
Convergence
Practice Questions
P (−1)n
1. Determine whether n
converges absolutely or conditionally.
P (−1)n
2. Test convergence of n2
.
P (−1)n
3. Does √
n
converge absolutely or conditionally?
P (−1)n
4. Apply the definition of absolute convergence to n3
.
P (−1)n
5. Approximate the sum of the first 5 terms of n
.
P (−1)n
6. Show that n
diverges absolutely.
P (−1)n P1
7. Compare n
with n
.
P (−1)n
8. Determine convergence of n1.5
.
P (−1)n
9. Use the ratio test to analyze n!
.
P (−1)n
10. Prove absolute convergence of n4
.
11. Show conditional convergence of the alternating harmonic series.
P (−1)n
12. Test convergence of n+1
.
P10 (−1)n
13. Approximate n=1 n
.
14. Explain why absolute convergence implies convergence.
15. Compare rearrangements of conditionally convergent series.
P (−1)n
16. Determine whether n1.01
converges absolutely.
P (−1)n
17. Show divergence of 3n .
√
P (−1)n
18. Apply the root test to 2n
.
1
