Ch.9 worksheet #1: Integral test and p

Ch.9 worksheet #1: Integral test and p-series test
Use the Integral Test to determine the convergence or divergence of the series.
1. Diverges
2. Diverges
3. Converges
4. Converges
5. Converges
6. Diverges
7. Diverges
8. Diverge
9. Diverges
10. Diverges
11. Diverges
12. Converges
13. Diverges
14. Converges
Explain why the Integral Test does not apply to the series.
16. an is not positive for all n
17. an is not positive for all n
18. an is not decreasing for all n
19. an is not decreasing for all n
Use the p-test to determine the convergence or divergence of the series.
20. Diverges
21. Converges
22. Converges
23. Diverges
24. Converges
25. Converges
Ch.9 worksheet #2: Direct and Limit Comparison Tests
Use the Direct Comparison Test to determine the convergence or divergence of the series.
1. Converges
3. Diverges
5. Converges
7. Converges
9. Diverges
2. Diverges
4. Converges
6. Converges
8. Diverges
10. Diverges
Use the Limit Comparison Test to determine the convergence or divergence of the series.
11. Diverges
13. Diverges
15.Converges
17. Converges
12. Converges
14. Diverges
16. Diverges
18. Converges
In exercise 22-28, test for convergence or divergence using each test at least once. Identify which test you used.
(a) Nth term Test for Divergence
(d) Integral Test
(b) P-series Test
(e) Direct Comparison Test
(c) Geometric Series Test
(f) Limit Comparison Test
19. Diverges
21. Converges
23. Diverges
20. Converges
22. Converges
24. Converges
Ch.9 worksheet #3: Alternating Series Test
Determine the convergence or divergence of the series.
1. Converges
4. Diverges
7. Converges
10. Converges
13. Converges
2. Diverges
5. Converges
8. Diverges
11. Diverges
14. Converges
3. Converges
6. Converges
9. Diverges
12. Diverges
15. Converges
Approximate the sum of the series by using the first 6 terms. Determine the accuracy of the approximation.
16. 2.4325, .0612
17. 2.7067, 1.0236
18. .07333, .002778
19. .1875, .05469
How many terms are needed to approximate the sum of the convergent series with an error less than .0001.
20. 7 terms, n = 6
21. 3 terms, n = 2
22. 1000 terms, n = 1000
23. 5 terms, n = 4
Determine whether the series converges conditionally, converges absolutely, or diverges.
24. Converges Absolutely
25. Converges Conditionally
26.
27. Converges Absolutely
28. Diverges
29.
30. Converges Conditionally
31. Converges Absolutely
32.
33. Converges Conditionally
34. Converges Conditionally
35.
Converges Conditionally
Diverges
Converges Absolutely
Converges Absolutely
Ch.9 worksheet #4: Ratio and Root Tests
Use the Ratio Test to determine the convergence or divergence of the series.
1. Diverges
2. Converges
4. Diverges
5. Converges
7. Converges (R Test Inconclusive)
8. Converges
10. Diverges
11. Converges
13. Converges
14. Converges
3. Converges
6. Diverges
9. Diverges
12. Diverges
15. Converges
Verify that the Ratio Test is inconclusive for the p-series.
16.
17.
18.
Use the Root Test to determine the convergence or divergence of the series.
19. Converges
20. Diverges
21. Diverges
22. Diverges
23. Converges
24. Diverges
25. Diverges
26. Converges
27. Converges
28. Converges
29. Converges
30. Diverges
Ch.9 worksheet #5: Convergence Tests
For 1 – 12, determine whether or not the series converge and state the test used.
1. Converges
4. Converges
7. Converges
10. Diverges
13. Converges conditionally
2. Converges
5. Diverges
8. Diverges
11. Diverges
3. Converges
6. Diverges
9. Converges
12. Converges
Ch.9 worksheet #6: Power Series
#1-4: Find a power series to represent the given function and identify the interval of convergence.
1. ∑
(
2. ∑
( ) ( )
3. ∑
( )
4. ∑
) (
(
)
)
5. ∑
a) ( )
b) ∑
(
c) ∑
( )
6. ∑
(
)
) (
)
a) ( )
b) ∑
c) ∑
(
(
)
(
)
)
7. Make up a geometric series ∑
a. ∑
8. False
11. A
that converges to 5.
b. ∑
( )
9. True
12. E
( )
10. C
13. D