ALTERNATING SERIES TEST Section 9 5 Calculus BC

SUMMARY OF TESTS FOR SERIES 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 2

ALTERNATING SERIES TEST 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 3

ALTERNATING SERIES TEST SUM 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 4

ALTERNATING SERIES TEST 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 5

ALTERNATING SERIES TEST EXAMPLES 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 6

ALTERNATING SERIES TEST 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 7

EXAMPLE 1 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 8

EXAMPLE 1 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 9

EXAMPLE 2 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 10

EXAMPLE 3 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 11

EXAMPLE 4 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 12

YOUR TURN 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 13

ALTERNATING HARMONIC SERIES A. Harmonic Series is where the sum takes a long time before approaching zero and therefore, the terms of the series diverges. B. Alternating Harmonic Series is like the harmonic series where the terms eventually (and slowly approach) where the terms of the series approach zero. The terms of the series converges. 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 14

EXAMPLE 5 12/15/2021 6: 08 AM § 9. 5: Alternating Series Test 15

EXAMPLE 5 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 16

YOUR TURN 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 17

YOUR TURN 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 18

ABSOLUTE VS CONDITIONAL CONVERGENCE 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 19

ABSOLUTE CONVERGENCE In absolutely convergent series, the terms are heading to terms of zero so quickly that sliding the terms around does not make any difference. In other words, addition in the absolutely convergent case follows the same rules of addition that we have always believed and treasured; addition is commutative for absolutely convergent series. Every rearrangement can be rearranged to have any sum. 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 20

CONDITIONAL CONVERGENCE In a conditionally convergent series, the terms can be rearranged to have any sum. 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 21

EXAMPLE 6 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 22

EXAMPLE 6 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 23

EXAMPLE 7 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 24

EXAMPLE 7 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 25

YOUR TURN 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 26

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) 12/15/2021 6: 09 AM § 9. 5: Alternating Series Test 27

AP MULTIPLE CHOICE PRACTICE QUESTION 1 (NON-CALCULATOR) Vocabulary 12/15/2021 6: 09 AM Connections and Process § 9. 5: Alternating Series Test Answer 28

ASSIGNMENT Page 625 5 -25 EOO, 27, 29, 37 -51 odd 12/15/2021 6: 10 AM § 9. 5: Alternating Series Test 29