AP Calculus BC Name CHAPTER 12A WORKSHEET INFINITE ...

AP Calculus BC

CHAPTER 12A WORKSHEET

INFINITE SEQUENCES AND SERIES

Name

Seat #

Date

Chapter 12A Review Sheet #2

Test each series for convergence or divergence. Identify the test used and show all your work.

1.

n2 1

n1 n 2 n

9.

n !

n0 2 5 8 ... 3n 2

2.

1

n1 n 2 n

10.

1

i1 i i 1

3.

3 k1

23k

k 1

11.

1n 21 n

n1

4.

k 1.7

k 1

12.

1k

ln

k

k 1

k

5.

n

en

n1

6.

2

n2 nln n3

13.

2 2n

nn

n1

14.

2 j

j1 2 j 1!

7.

3n n2

n1 n !

15.

n 2 1 n

n1

8.

3 j

j1 5 j j

16. sin n n1

AP Calculus BC

CHAPTER 12A WORKSHEET

INFINITE SEQUENCES AND SERIES

Chapter 12A Review Sheet #2

ANSWER KEY

1. Diverges by nth term test.

9. Converges by ratio test.

2. Converges by either direct or limit

comparison with 1

n 2

n1

10. Diverges by limit comparison with harmonic series.

3. Converges by alternating series or ratio 11. Diverges by nth term test. test or rewriting as geometric series.

4. Converges: p-series.

12. Converges: alternating series.

5. Converges by ratio test or root test.

13. Converges by root test.

6. Converges by integral test.

14. Converges by ratio test.

7. Converges by ratio test.

15. Converges by root test.

8. Converges by direct comparison with

3 n

n1 5

16. Diverges by nth term test.

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