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Sec 11.7: Strategy for Testing Series Series Tests 1)Test for Divergence 2) Integral Test 3) Comparison Test 4) Limit Comparison Test 5) Ratio Test 6)Root.

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Presentation on theme: "Sec 11.7: Strategy for Testing Series Series Tests 1)Test for Divergence 2) Integral Test 3) Comparison Test 4) Limit Comparison Test 5) Ratio Test 6)Root."— Presentation transcript:

1 Sec 11.7: Strategy for Testing Series Series Tests 1)Test for Divergence 2) Integral Test 3) Comparison Test 4) Limit Comparison Test 5) Ratio Test 6)Root Test 7)Alternating Series Test Special Series: 1)Geometric Series 2)Harmonic Series 3)Telescoping Series 4)p-series

2 Sec 11.7: Strategy for Testing Series 5-types 1) Determine whether convg or divg 2) Find the sum s 3) Estimate the sum s 4) How many terms are needed within error 5) Partial sums

3 STRATEGY FOR TESTING SERIES p-series geometric Similar to geom or p-series Use Comparison or Limit Comparison Test for Divergence Alternating Ratio TestRoot Test easy to integrate Integral Test telescoping Sec 11.7: Strategy for Testing Series

4 TERM-091 Sec 11.7: Strategy for Testing Series

5 TERM-082 Sec 11.7: Strategy for Testing Series

6 TERM-101 Sec 11.7: Strategy for Testing Series

7 TERM-102 Sec 11.7: Strategy for Testing Series

8 TERM-102 Sec 11.7: Strategy for Testing Series Remark: All terms are not positive

9 TERM-091 Sec 11.7: Strategy for Testing Series

10 TERM-082 Sec 11.7: Strategy for Testing Series

11 TERM-091 Sec 11.7: Strategy for Testing Series

12 TERM-091 Sec 11.7: Strategy for Testing Series

13 TERM-082 Sec 11.7: Strategy for Testing Series

14 TERM-102 Sec 11.7: Strategy for Testing Series Remark: All terms are not positive

15 TERM-082 Sec 11.7: Strategy for Testing Series

16 TERM-102 Sec 11.7: Strategy for Testing Series

17 TERM-102 Sec 11.7: Strategy for Testing Series

18 TERM-092 Sec 11.7: Strategy for Testing Series

19 TERM-082 Sec 11.7: Strategy for Testing Series

20 5-types 1) Determine whether convg or divg 2) Find the sum s 3) Estimate the sum s 4) How many terms are needed within error 5) Partial sums

21 Geometric Series: 2) Find the sum s Telescoping Series: Convergent nth-partial sums : DEF: Given a seris

22 nth-partial sums : DEF: Given a seris 3) Estimate the sum s

23 TERM-101

24 TERM-091 Sec 11.7: Strategy for Testing Series

25 Final-092

26 4) How many terms are needed within error REMAINDER ESTIMATE FOR THE INTEGRAL TEST THEOREM: (ALTERNATING SERIES ESTIMATION THEOREM)

27 REMAINDER ESTIMATE FOR THE INTEGRAL TEST

28 THEOREM: (ALTERNATING SERIES ESTIMATION THEOREM) TERM-102

29 TERM-101 nS_n|R_n|b_(n+1) 7-0.113931290322100.00115825660.0019569 8-0.115888237484530.00079869050.0013736 10-0.115515612111900.00042606510.0007518 12-0.115342771208250.00025322420.0004553 999-0.11508905392165 1000-0.11508905492165

30 TERM-092

31

32 Sec 11.7: Strategy for Testing Series 5-types 1) Determine whether convg or divg 2) Find the sum s 3) Estimate the sum s 4) How many terms are needed within error 5) Partial sums

33 Geometric Series: Telescoping Series: DEF: Given a seris

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