SERIES AND CONVERGENCE Section 9 2 Calculus BC

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SERIES AND CONVERGENCE Section 9. 2 Calculus BC AP/Dual, Revised © 2016 viet. dang@humble.

SERIES AND CONVERGENCE Section 9. 2 Calculus BC AP/Dual, Revised © 2016 viet. dang@humble. k 12. tx. us 12/15/2021 7: 18 PM 9. 2: Series and Convergence 1

SUMMARY OF TESTS FOR SERIES 12/15/2021 7: 18 PM 9. 2: Series and Convergence

SUMMARY OF TESTS FOR SERIES 12/15/2021 7: 18 PM 9. 2: Series and Convergence 2

DEFINITIONS 12/15/2021 7: 18 PM 9. 2: Series and Convergence 3

DEFINITIONS 12/15/2021 7: 18 PM 9. 2: Series and Convergence 3

WHAT IS SIGMA NOTATION? Upper Limit Function Lower Limit Known as “index” 12/15/2021 7:

WHAT IS SIGMA NOTATION? Upper Limit Function Lower Limit Known as “index” 12/15/2021 7: 18 PM Summation 9. 2: Series and Convergence 4

EXAMPLE 1 12/15/2021 7: 18 PM 9. 2: Series and Convergence 5

EXAMPLE 1 12/15/2021 7: 18 PM 9. 2: Series and Convergence 5

GEOMETRIC SERIES TEST 12/15/2021 7: 18 PM 9. 2: Series and Convergence 6

GEOMETRIC SERIES TEST 12/15/2021 7: 18 PM 9. 2: Series and Convergence 6

EXAMPLE 2 12/15/2021 7: 18 PM 9. 2: Series and Convergence 7

EXAMPLE 2 12/15/2021 7: 18 PM 9. 2: Series and Convergence 7

EXAMPLE 2 12/15/2021 7: 18 PM 9. 2: Series and Convergence 8

EXAMPLE 2 12/15/2021 7: 18 PM 9. 2: Series and Convergence 8

EXAMPLE 3 12/15/2021 7: 18 PM 9. 2: Series and Convergence 9

EXAMPLE 3 12/15/2021 7: 18 PM 9. 2: Series and Convergence 9

YOUR TURN 12/15/2021 7: 18 PM 9. 2: Series and Convergence 10

YOUR TURN 12/15/2021 7: 18 PM 9. 2: Series and Convergence 10

NTH TERM TEST FOR DIVERGENCE 12/15/2021 7: 18 PM 9. 2: Series and Convergence

NTH TERM TEST FOR DIVERGENCE 12/15/2021 7: 18 PM 9. 2: Series and Convergence 11

EXAMPLE 4 12/15/2021 7: 18 PM 9. 2: Series and Convergence 12

EXAMPLE 4 12/15/2021 7: 18 PM 9. 2: Series and Convergence 12

EXAMPLE 5 12/15/2021 7: 18 PM 9. 2: Series and Convergence 13

EXAMPLE 5 12/15/2021 7: 18 PM 9. 2: Series and Convergence 13

EXAMPLE 6 12/15/2021 7: 18 PM 9. 2: Series and Convergence 14

EXAMPLE 6 12/15/2021 7: 18 PM 9. 2: Series and Convergence 14

EXAMPLE 6 12/15/2021 7: 18 PM 9. 2: Series and Convergence 15

EXAMPLE 6 12/15/2021 7: 18 PM 9. 2: Series and Convergence 15

YOUR TURN 12/15/2021 7: 18 PM 9. 2: Series and Convergence 16

YOUR TURN 12/15/2021 7: 18 PM 9. 2: Series and Convergence 16

TELESCOPING TEST A. B. C. D. E. Known as the terms “collapse” to one

TELESCOPING TEST A. B. C. D. E. Known as the terms “collapse” to one term or several terms Uses the associative property of addition Series collapses to a finite sum To get the sum, start plugging in numbers Hint: Generally has two ratios associated with Telescoping Series when generating the sum 12/15/2021 7: 18 PM 9. 2: Series and Convergence 17

EXAMPLE 7 12/15/2021 7: 18 PM 9. 2: Series and Convergence 18

EXAMPLE 7 12/15/2021 7: 18 PM 9. 2: Series and Convergence 18

EXAMPLE 8 12/15/2021 7: 18 PM 9. 2: Series and Convergence 19

EXAMPLE 8 12/15/2021 7: 18 PM 9. 2: Series and Convergence 19

EXAMPLE 8 12/15/2021 7: 19 PM 9. 2: Series and Convergence 20

EXAMPLE 8 12/15/2021 7: 19 PM 9. 2: Series and Convergence 20

EXAMPLE 8 12/15/2021 7: 19 PM 9. 2: Series and Convergence 21

EXAMPLE 8 12/15/2021 7: 19 PM 9. 2: Series and Convergence 21

EXAMPLE 8 12/15/2021 7: 19 PM 9. 2: Series and Convergence 22

EXAMPLE 8 12/15/2021 7: 19 PM 9. 2: Series and Convergence 22

YOUR TURN 12/15/2021 7: 19 PM 9. 2: Series and Convergence 23

YOUR TURN 12/15/2021 7: 19 PM 9. 2: Series and Convergence 23

ASSIGNMENT Page 601 7 -19 odd, 25 -31 odd, 41 -53 odd 12/15/2021 7:

ASSIGNMENT Page 601 7 -19 odd, 25 -31 odd, 41 -53 odd 12/15/2021 7: 19 PM 9. 2: Series and Convergence 24

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