1. C HAPTER 9-H S TRATEGIES FOR T ESTING SERIES

2. Strategies Classify the series to determine which test to use. 1. If then the series diverges. This is the nth Term Test for divergence. 2. Look to see if the series is a p-series. If so it will converge if p > 1 and diverge if p ≤ 1. 3. Look to see if the series is a geometric series. If so it will converge if r < 1. If r ≥ 1 then it will diverge. ( you may need to manipulate the series algebraically to get it into the proper form)

3. Strategies cont. 4. If your series is similar to a p-series or a geometric series try a comparison test. Applies only to series with positive terms 5. If the terms of your series alternate between positive and negative try the alternating series test.

4. Strategies cont. 6. If your series contains factorials or a constant raised to the power n try the ratio test (but don’t bother with the ratio test for a p-series). 7. If the series is of the form Ʃ (b n ) n try the root test. 8. If a n = f(n) where is easily evaluated try the integral test. 9. Telescoping series: write out series and cancel terms

5. 1.

6. 2.

7. 2 cont. Find the limit

8. 3.

9. 4.

10. 4. cont.

11. 4. cont

12. 5.

13. 5. cont

15. 6.

16. 6. cont

17. 7.

18. 8. Determine the convergence or divergence of the series

19. 9. Determine the convergence or divergence of the series

20. 10. Determine the convergence or divergence of the series

21. 11. Determine the convergence or divergence of the series

22. 12. Determine the convergence or divergence of the series

23. H OME W ORK Worksheet 9-H