Sequences
Sequences
Build intuition for discrete patterns and their limits
Learn convergence, tests, and applications from finance to growth models.
Course Highlights
- View sequences as functions on ; connect discrete steps to continuous ideas.
- Understand convergence through – intuition and classic test cases.
- Meet arithmetic/geometric patterns, recurrence relations, and real-world growth/decay models.
- Practice-driven: short exercises with explanations in each chapter.
Sequence limits are the front door to calculus—master them and the rest of analysis feels friendlier.
Author’s Note
Every sequence hides a rule—like footsteps toward an unseen destination. Don’t stare at a single term; look ahead to the limit.
总结
本文出现的符号
| 符号 | 类型 | 读音/说明 | 在本文中的含义 |
|---|---|---|---|
| 数学符号 | natural numbers | 作为索引的正整数集合 | |
| 数学符号 | Real numbers | 实数集合，项的取值范围 | |
| 数列记号 | a sub n | 第 项 | |
| 数列记号 | sequence a_n | 整个数列 |
中英对照
| 中文术语 | 英文术语 | 音标 | 说明 |
|---|---|---|---|
| 数列 | sequence | /ˈsiːkwəns/ | 以正整数为索引的函数 |
| 极限 | limit | /ˈlɪmɪt/ | 项趋近某值的过程 |
| 收敛 | convergence | /kənˈvɜːrdʒəns/ | 数列极限存在的性质 |
| 发散 | divergence | /daɪˈvɜːrdʒəns/ | 数列没有有限极限 |
| 通项 | general term | /ˈdʒenərəl tɜːrm/ | 直接给出第 项的表达式 |
Chapters
课程路线图
- 1
Exploring Functions in Advanced Mathematics
先修课程Functions are a core idea of advanced mathematics. This course walks through foundational concepts, key properties, and classic constants so you can read, reason, and compute with confidence.
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Sequences
当前课程Sequences bridge discrete thinking and calculus. This track covers core definitions, limits, convergence, and classic models.
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