Welcome to Unit 2 - Series & Convergence of AP Calculus BC

I'm so excited to "see" new faces and returning students. I will do my best to create a positive learning environment for each of you.
Most weeks we will utilize handfuls of technological tools.

Most Daily/ Weekly assignments will be due the next day.

Listed below will be our Daily Agenda Activities for our "class days" of Monday - Friday.
Tuesday or Thursday Afternoon Office Time (2:30pm - 3:00pm)

Be Your Best, Do Your Best, & Breathe!

Free Printable Graph Paper

Unit 2 & Unit 3
- Series & Convergence
Objectives

Students will be able to:

4.1A1: The nth partial sum is defined as the sum of the first n terms of a sequence.

4.1A2: An infinite series of numbers converges to a real number (or has sum ), if and only if the limit of its sequence of partial sums exists and equals.

4.1A3: Common series of numbers include geometric series, the harmonic series, and p-series.

4.1A4: A series may be absolutely convergent, conditionally convergent, or divergent.

4.1A5: If a series converges absolutely, then it converges.

4.1A6: In addition to examining the limit of the sequence of partial sums of the series, methods for determining whether a series of numbers converges or diverges are the nth term test, the comparison test, the limit comparison test, the integral test, the ratio test, and the alternating series test.

4.1B1: If is a real number and is a real number such
that, then the geometric series.

4.1B2: If an alternating series converges by the alternating series test, then the alternating series error bound can be used to estimate how close a partial sum is to the value of the infinite series.

4.1B3: If a series converges absolutely, then any series obtained from it by regrouping or rearranging the terms has the same value.

Unit 2 – Quote – “Believe in Yourself and all that you are. Know that there is something
inside you that is greater than any obstacle.” – Christian D. Larson

Weekly Calendar & Homework

	Feb 14^th	Feb 15^th	Feb 16^th	Feb 17^th	Feb 18^th
Unit 2 & 3 Packet PDF Version
AP Calculus BC Topic/Concept	Integral Test	nth Term Test, p - Series, & Review	nth Term Test, p - Series, & Review	Unit Test # 2	Workday
Week 5
4^th Period	1. Discuss Quiz results & Student Sample Examples 2. Discuss Multiple Intelligence Survey Results & Additional Info 3. Divide the class into 4 Project Groups 4. Determine the 12 "Easily Integrable" problems from the Worksheet. 5. Series Test Review Worksheet = Groups of 2	1. Discuss Multiple Intelligence Group Project/Quiz Guidelines w/Seasonal Themes 2. Take Notes on the Video for the nth Term Series Test 3. nth Term Examples = Worksheet Packet Pages 21 - 22 4. Take Notes on the Video for the p-series Test 5. Read p-series notes = Worksheet Packet Page 26 6. Series Test Review Worksheet = Groups of 2 7. Song Time!	1. Discuss Jamboard HW 2. In-Class Kahoot - Review 3. In - class Short Kahoot 4. In-Class Classwork Grade = n^th & p-Series Upload 5. Series Test Review & Discuss results	Unit Test 2 Link
	- Day 11 Upload Link for the 12 Integral Series Problems & the "Special nth Term Case" Problems - Put the 12 Integral Test Homework Problems & the Special Cases on the Jamboard for Wednesday's Class by 7:00 am Integral Homework Problems - 3 of the Slides should be blank.	- Canvas Circuit Upload & p-Series Investigation Upload due Tuesday 2/22 by 7 am Problem Set # 2 due Feb 22^nd by 4pm ( AP Central Problems) AP Central Login Code: X7E27A = Classwork Grade	well and ! - Tuesday's HW	Give a Smile to 3 Different People (❁´◡`❁) - Tuesday's HW - Read over the Multiple Intelligence Article - Favorite Season Survey due 2/25
Calculus Songs	Twinkle Writing # 38 - Tune Twinkle Twinkle Little Star	Mathematical Christmas Carol: Calculus # 36 - Tune Jingle Bells	I Can See Reason # 34 - Tune I Saw the Light
National Events	February 14 Cream-Filled Chocolates Day Ferris Wheel Day Organ Donor Day Valentines Day Clean Out Your Computer Day	February 15 Gumdrop Day	February 16 Almond Day Do A Grouch a Favor Day Pancake Day – IHOP	February 17 Random Acts of Kindness Day Cabbage Day	February 18 Battery Day Crab Stuffed Flounder Day Caregivers Day February 19 Arabian Horse Day Chocolate Mint Day Lash Day February 20 Comfy Day Cherry Pie Day Love Your Pet Day Muffin Day

6. Stay Safe, Do Your Best, Give Your Best,

Additional Resources, Previous Skill Review, & Picture Examples Below:

AP Calculus BC - "Paul's Notes" - Website Link

Review Links with Practice Problems	Video Reviews
Review # 1 - Root Test Review # 2 = Improper Integrals Review # 3 = Direct & Limit Comparison Test Review # 4 = Telescoping Series & Geometric Series	Review #5 - nth Term Series Test Review # 6 - p-series Test Review #7 - Integral Test Review # 8 - Ratio Test Review # 9 - Telescoping Series Review # 10 - Root Test

AP Central Video Resources AP Central Login Code: X7E27A	6.14 Selecting Techniques for Antidifferentiation	10.5 p-Series Test
3.3 Differentiating Inverse Function Video 1 & Video 2	10.1 Defining Converging and DIverging Infinite Series	10.6 Direct Comparison Test
3.4 Differentiating Trig Inverse Functions Video 1 & Video 2	10.2 Geometric Test	10.6 Limit Comparison Test
6.7 Fundamental Theorem of Calculus	10.3 nth Term Test	10.7 Alternating Series Test
6.10 Trig Substitution	10.4 Integral Test	10.9 Alternating Conditions
6.13 Improper Integrals Video 1 & Video 2		10.8 Ratio Test

Keep up the Good Work for this Semester in All of Your Classes!