AP Comp Sci A Homework - Block D

1. 9.2 Series and Convergence
   1. Geometric Series
   2. Limit of nth term of a Convergent Series Th,
   3. nth term test for Divergence
2. ∆Math Lab 2-1 (9.1-9.2)

1. Wikibooks: Sequence
2. Wikibooks: Series
3. Orders of Growth Poster

4. Order of Magnitude WS

5. Cesàro Summation and Analytic Continuation Video

6. Divergent Infinite Sums BriTheMathGuy Video

1. The Harmonic Series | Illustrated Theory of Music #8
2. Proofs that the Harmonic Series Diverges:
   1. Goldmakher's Short Proof
   2. Proofs part 1
   3. Proofs 2
   4. ∆Math HW Q 2-3 (ch 9.1-9,2)
3. Slides :Geometric, nth term, Integral Test, p test (92.-9.3 pdf) (keynote)

For HW

1. Textbook Problems
2. ∆Math Lab 2-2: Integral Tests

1. Convergence Test Table 1

2. Convergence Table 2

3. n-term Div wikibooks on nth Term Test for Divergence
4. Geometric Series from Ximera
5. p-series @17Calc
6. Integral Test from former 17Calc

1. Orders of Growth Poster
   

2. Order of Magnitude WS

1. Convergence Tests (pdf)
2. WikiBook's Integral Test
3. XIMERA: Integral Test

1. Convergent Series at Wikibook
2. Wikibooks: Series
3. Wikibooks: Integral Test
4. XIMERA: Integral Test

1. FRQ Quiz on sequences, n-th term, p-series, geometric, and Integral tests.
2. Direct Comparison Test (DCT)
3. Limit Comparison Test (LCT)
4. DCT from former@ 17Calc
5. LCT from former 17Calc

1. Convergence Test Table 1
   
2. Convergence Table 2
   
3. Convergence WS
4. Video: LCT Proof

1. XIMera: DCT

1. Q 2-5 (9.1-9.4)
2. Intro to AST Alternating Series WS
3. AST Slides
4. AST Practice
5. Exercises from former 17Calculus

1. Textbook Exercises
2. ∆Math Lab: LCT/AST (Lab 2-4 and 2-5)

1. AST Examples

2. AST Remainder/Error Estimation

3. Alternating Series Test Practice

4. Cool Fact about conditionally convergent series
   

1. Did you do the AMC 10/12 in 2024?

   Then LOGIN HERE before using the next link for today's competition

2. SFHS Registration for AMC 12B(November 13, 2025)

AMC 12B: November 13, 2025

Free Math Jams

(not free) 2 Day Online Preparation Seminars

AMC 12 at AoPS

1. Review of Convergence Tests - How to pick the right one
2. Absolute vs Conditional Convergence
3. Which Test is Best #1
4. Which Test is Best #2?
5. Flowchart 1
6. Flowchart 2
7. Flowchart 3
8. HWQ on Ratio/Root Tests
9. Ch 9 MC Practice with answers

1. Convergence Test Strategy Video

2. Series Test Practice WS

3. Summary by Cal-Tech student Laura Shou

4. David Mao Examples of comparison Tests

5. Calc 13 Summary

1. Convergence WS
   
2. Ratio Test Practice
   

In class

1. HWQ 2-6 (Paper) and/or Q 2-7 (∆Math)
2. Root/Ratio/Interval of Convergence (page 9-13)
3. Seq and Seiries - formerly @ 17 Calc
4. AMC 12 A 2025: Preliminary Results (no awards or AIME Qualifier info available yet)
5. AMC 12A 2025 Solutions

1. Textbook problems
2. Lab 2-6: Ratio Test

1. Did you do the AMC 10/12 in 2024?

   Then LOGIN HERE before using the next link for today's competition

2. SFHS Registration for AMC 12B(November 13, 2025)

AMC 12B: November 13, 2025

Free Math Jams

(not free) 2 Day Online Preparation Seminars

AMC 12 at AoPS

• Past AMC 12 Questions and Solutions

1. Get the KhanApp

2. Chapter 9 Stuff at Khan

3. Sequences from Ximera
4. n-th Term Test

5. Geometric Series from Ximera

6. Telescoping Series

7. Integral Test

8. DCT

9. LCT

10. AST

11. Ratio Rest

12. Root Test

13. Interval of Convergence

1. Series Test Practice WS

2. Summary

3. David Mao Examples of comparison Tests

4. Sequence and Series Exercises from Wikibooks Has hints, answers, and Full Solutions

1. Examples of Taylor Series Questions (∆Math)
2. Taylor Series Practice (∆Math)
3. Taylor WS 1
4. Taylor Polynomials 2 WS.pdf
   
5. Legrange Error (Taylor Theorem)

• Does the Alternating series ever fail? (ppt)

• Does the Alt Series Remainder ever Fail? (video)
• Error Bounds In Power Series WS

• Fill in the Paper Worksheet "Introduction to Taylor Series" (At least up to page 6)
• Bring this to class Nov 20

1. Examples of Taylor Series Questions (∆Math)
2. Taylor Series Practice (∆Math)
3. Taylor WS 1
4. Taylor Polynomials 2 WS.pdf
   
5. Legrange Error (Taylor Theorem)

For HW

• Textbook Problems
• Lab 2-7 Practice Taylor Series (∆Math)

1. TaylorPolynomials1WS.pdf
   
2. Taylor Polynomials 2 WS.pdf
   
3. Lagrange Remainder WS.pdf
   

In class

1. HWQ 2-13(∆Math)
2. 9.8 Power Series: Intervals of Convergence
3. 9.9 Representation of Functions by Power Series

Textbook exercises
2. BC Lab: Power Series (∆ Math)

1. Collaborative Proof of Euler's Equation e^πi+1 = 0
2. HWQ 2-14 (Paper)
3. Worksheet 3 on Series
   (Here are answers to check your work)
4. Error Bounds WS ( filled in)

1. p 680 from Text Book
2. Finish Worksheet 3 on Series
   (Here are answers to check your work)

1. Gotta No
2. Fill in version
3. Ch 9 MC Practice with answers

1. Get the KhanApp

2. Chapter 9 Stuff at Khan

3. Sequences from Ximera
4. n-th Term Test

5. Sequences from Ximera
6. Geometric Series from Ximera

1. Class 2-18 at AP Classroom
2. Sem 1 FRQ
3. Unit 10 Progress Check: MCQ Part A
4. Unit 10 Progress Check: MCQ Part B
5. Unit 10 Progress Check: MCQ Part C

1. Review
2. Q 2-16 on 9B
3. Unit 10 Progress Check: MCQ Part A, B, C (AP Classroom)