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Sec 11.7: Strategy for Testing Series

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Presentation on theme: "Sec 11.7: Strategy for Testing Series"— Presentation transcript:

1 Sec 11.7: Strategy for Testing Series
Special Series: Series Tests Geometric Series Harmonic Series Telescoping Series p-series Test for Divergence Integral Test Comparison Test Limit Comparison Test Ratio Test Root Test Alternating Series Test

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

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

4 Sec 11.7: Strategy for Testing Series
TERM-091

5 Sec 11.7: Strategy for Testing Series
TERM-082

6 Sec 11.7: Strategy for Testing Series
TERM-101

7 Sec 11.7: Strategy for Testing Series
TERM-102

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

9 Sec 11.7: Strategy for Testing Series
TERM-091

10 Sec 11.7: Strategy for Testing Series
TERM-082

11 Sec 11.7: Strategy for Testing Series
TERM-091

12 Sec 11.7: Strategy for Testing Series
TERM-082

13 Sec 11.7: Strategy for Testing Series
TERM-102

14 Sec 11.7: Strategy for Testing Series
TERM-092

15 5-types 1) Determine whether convg or divg 2) Find the sum s
Sec 11.7: Strategy for Testing Series 1) Determine whether convg or divg 2) Find the sum s 5-types 5) Partial sums 3) Estimate the sum s 4) How many terms are needed within error

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

17 5) Partial sums DEF: Given a seris Geometric Series:
Telescoping Series:

18 Telescoping Series:

19 Note: Sec 5.3: THE FUNDAMENTAL THEOREM OF CALCULUS
THE FUNDAMENTAL THEOREM OF CALCULUS, PART 1 Note:

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24 Integration Techniques
Sec 7.5: STRATEGY FOR INTEGRATION Integration Techniques Partial fraction susbsit Trig subs rational sine&cos Trig fns by parts rational sine&cos back 2 original

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64 Quiz Material Rieman sum Ch8 Improper Integral Fud. Thm of Calculus Integration by parts Volume of solid Taylor series 1/x Interval of convergence Conditional convg + Abs. convg Integration:

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