Sequences

Build intuition for discrete patterns and their limits

Learn convergence, tests, and applications from finance to growth models.

Sequence basicsLimitsConvergenceApplications

Course Highlights

View sequences as functions on $\mathbb{N}$ ; connect discrete steps to continuous ideas.
Understand convergence through $\varepsilon$ – $N$ 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.

Every sequence hides a rule—like footsteps toward an unseen destination. Don’t stare at a single term; look ahead to the limit.

符号	类型	读音/说明	在本文中的含义
$\mathbb{N}$	数学符号	natural numbers	作为索引的正整数集合
$\mathbb{R}$	数学符号	Real numbers	实数集合，项的取值范围
$a_n$	数列记号	a sub n	第 $n$ 项
$\{a_n\}$	数列记号	sequence a_n	整个数列

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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2
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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