Radius of Convergence
Core Sentence / 核心句
The radius of convergence is how far from the center a power series converges.
中文理解：收敛半径表示从中心点往左右多远以内 power series 会收敛。
Formula / 公式或规则
Find the open interval first, usually by Ratio Test; the radius is half the interval length.
When To Use / 什么时候用
看到 power series centered at 、find radius，就求 radius of convergence。
Watch Out / 易错点
radius 不包括 endpoint behavior；endpoint belongs to interval of convergence.
Search and Source Mentions / 搜索与出现位置
Mentioned In / 出现位置
- Chapter 11 · Local Information Has Limited Reach
- the Taylor series for about 1 converges only within a limited distance from its center
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · 8. Interval and Radius of Convergence / 收敛区间与半径
8. Interval and Radius of Convergence / 收敛区间与半径
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · Knowledge Point 20: Power Series Depends on x
- Radius of Convergence：离 center 多远还能收敛
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · 12. Confusion / Questions
12. radius of convergence 和 interval of convergence 有什么关系？
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · 3. Class Flow / 课堂脉络
13. 讲 Interval of Convergence 和 Radius of Convergence。