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 transcript:

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

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

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

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 Sec 11.7: Strategy for Testing Series

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

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 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

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

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

Telescoping Series:

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

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

Quiz Material 1)Rieman sum 2)Ch8 3)Improper Integral 4)Fud. Thm of Calculus 5)Integration by parts 6)Volume of solid 7)Taylor series 1/x 8)Interval of convergence 9)Conditional convg + Abs. convg Integration: