Practice Problems: Alternating Series
Practice Questions
(−1)n+1 n1 converges.
P
1. Determine whether
Test convergence of (−1)n n12 .
P
2.
Does (−1)n+1 √1n converge?
P
3.
Apply the Alternating Series Test to (−1)n n13 .
P
4.
Approximate the sum of the first 5 terms of (−1)n+1 n1 .
P
5.
Estimate the error after 10 terms of (−1)n+1 n1 .
P
6.
n
Show divergence of (−1)n n+1
P
7. .
Compare (−1)n n1 with
P P1
8. n
.
Use the error bound to approximate (−1)n n12 with 20 terms.
P
9.
Prove convergence of (−1)n n14 .
P
10.
1
Determine divergence of (−1)n √
P
11. 3 n.
Apply the Limit Comparison Test to (−1)n n21+5 .
P
12.
Approximate 10 n1
P
13. n=1 (−1) n .
1
Show convergence of (−1)n n1.5
P
14. .
Compare growth of partial sums for (−1)n n1 and (−1)n n12 .
P P
15.
1
Find whether (−1)n n1.01
P
16. converges.
Estimate the error in approximating (−1)n n12 with 15 terms.
P
17.
Show that (−1)n n!1 converges absolutely.
P
18.
Explain why (−1)n n1 converges conditionally but not absolutely.
P
19.
Compare approximation accuracy using 5 vs 10 terms of (−1)n n1 .
P
20.
1
Practice Questions
(−1)n+1 n1 converges.
P
1. Determine whether
Test convergence of (−1)n n12 .
P
2.
Does (−1)n+1 √1n converge?
P
3.
Apply the Alternating Series Test to (−1)n n13 .
P
4.
Approximate the sum of the first 5 terms of (−1)n+1 n1 .
P
5.
Estimate the error after 10 terms of (−1)n+1 n1 .
P
6.
n
Show divergence of (−1)n n+1
P
7. .
Compare (−1)n n1 with
P P1
8. n
.
Use the error bound to approximate (−1)n n12 with 20 terms.
P
9.
Prove convergence of (−1)n n14 .
P
10.
1
Determine divergence of (−1)n √
P
11. 3 n.
Apply the Limit Comparison Test to (−1)n n21+5 .
P
12.
Approximate 10 n1
P
13. n=1 (−1) n .
1
Show convergence of (−1)n n1.5
P
14. .
Compare growth of partial sums for (−1)n n1 and (−1)n n12 .
P P
15.
1
Find whether (−1)n n1.01
P
16. converges.
Estimate the error in approximating (−1)n n12 with 15 terms.
P
17.
Show that (−1)n n!1 converges absolutely.
P
18.
Explain why (−1)n n1 converges conditionally but not absolutely.
P
19.
Compare approximation accuracy using 5 vs 10 terms of (−1)n n1 .
P
20.
1
