AP Exam Weight: 15-25% | Multiple Choice: 6-10 questions | Free Response: Usually 1 full question

📚 Table of Contents

1. [Sequence Basics]
2. [Series Tests]
3. [Power Series]
4. [Taylor Series]
5. [Error Bounds]

1. Sequence Basics 📊

Understanding Sequences

A sequence is a list of numbers in order. Think of it as:

• Pattern of values following a rule
• Function with domain of natural numbers
• Stepping stones to series
• Ordered list of terms

Basic Concepts

Notation

• {aₙ} represents a sequence
• aₙ is the nth term
• Explicit vs. recursive form
• Index notation

Example Walkthrough

Find the first 4 terms of aₙ = n²/(n+1)

1. n = 1:

• a₁ = 1²/(1+1) = 1/2

2. n = 2:

• a₂ = 2²/(2+1) = 4/3

3. n = 3:

• a₃ = 9/4

4. n = 4:

• a₄ = 16/5

Convergence of Sequences

Process for Finding Limits