Sec 11.7: Strategy for Testing Series

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Presentation transcript:

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

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

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

Sec 11.7: Strategy for Testing Series TERM-091

Sec 11.7: Strategy for Testing Series TERM-082

Sec 11.7: Strategy for Testing Series TERM-101

Sec 11.7: Strategy for Testing Series TERM-102

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

Sec 11.7: Strategy for Testing Series TERM-091

Sec 11.7: Strategy for Testing Series TERM-082

Sec 11.7: Strategy for Testing Series TERM-091

Sec 11.7: Strategy for Testing Series TERM-082

Sec 11.7: Strategy for Testing Series TERM-102

Sec 11.7: Strategy for Testing Series TERM-092

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

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

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

Telescoping Series:

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

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

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: