Practice Problems: P-Series
Practice Questions
1
P
1. Determine whether n3
converges or diverges.
1
P
2. Test convergence of n0.8
.
P 1
3. Does n2 +1
converge?
P 1
4. Compare np
for p = 1.5 and p = 0.5.
P 1
5. Use the Integral Test to analyze n1.2
.
P 1
6. Approximate the sum of the first 10 terms of n2
.
P1
7. Show that n
diverges.
P 1 P 1
8. Compare n2
with n3
.
P 1
9. Estimate the remainder after 50 terms of n2
.
P 1
10. Prove convergence of n4
.
P 1
11. Determine divergence of √ .
n
P 1
12. Apply the Limit Comparison Test to n2 +5
.
13. Approximate 100 1
P
n=1 n2 .
P 1
14. Show divergence of n0.9
.
P 1 R∞
15. Compare n2
with the integral 1 x12 dx.
P 1
16. Find whether np
converges for p = 1.01.
P 1
17. Estimate the error in approximating n2
with 20 terms.
P 1
18. Show that n5
converges absolutely.
P1
19. Explain why n
diverges even though terms go to zero.
20. Compare growth of partial sums for p = 2 and p = 0.5.
1
Practice Questions
1
P
1. Determine whether n3
converges or diverges.
1
P
2. Test convergence of n0.8
.
P 1
3. Does n2 +1
converge?
P 1
4. Compare np
for p = 1.5 and p = 0.5.
P 1
5. Use the Integral Test to analyze n1.2
.
P 1
6. Approximate the sum of the first 10 terms of n2
.
P1
7. Show that n
diverges.
P 1 P 1
8. Compare n2
with n3
.
P 1
9. Estimate the remainder after 50 terms of n2
.
P 1
10. Prove convergence of n4
.
P 1
11. Determine divergence of √ .
n
P 1
12. Apply the Limit Comparison Test to n2 +5
.
13. Approximate 100 1
P
n=1 n2 .
P 1
14. Show divergence of n0.9
.
P 1 R∞
15. Compare n2
with the integral 1 x12 dx.
P 1
16. Find whether np
converges for p = 1.01.
P 1
17. Estimate the error in approximating n2
with 20 terms.
P 1
18. Show that n5
converges absolutely.
P1
19. Explain why n
diverges even though terms go to zero.
20. Compare growth of partial sums for p = 2 and p = 0.5.
1
