Interval of Convergence
Core Sentence / 核心句
The interval of convergence is the set of x-values where a power series converges.
中文理解：收敛区间回答的是：哪些 代进去后这个 power series 会收敛。
Formula / 公式或规则
Usually found by Ratio Test first, then endpoint testing.
When To Use / 什么时候用
看到 power series、find interval、endpoint，就找 interval of convergence。
Watch Out / 易错点
Ratio Test 给的是 open interval；端点必须单独代回原 series 检查。
Search and Source Mentions / 搜索与出现位置
Mentioned In / 出现位置
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · 6. The interval of convergence requires endpoint testing.
6. The interval of convergence requires endpoint testing.
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · Knowledge Point 20: Power Series Depends on x
- Interval of Convergence：哪些 $x$ 让级数收敛
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · Knowledge Point 17: Series Can Be Differentiated and Integrated
The power series is equal to the function on its interval of convergence.
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · Knowledge Point 22: Always Check Endpoints
\text{interval of convergence}=(2,4)
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · 12. Confusion / Questions
11. 为什么 interval of convergence 一定要 check endpoints？
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · Taylor / Maclaurin Map
Need interval of convergence?
- 微积分BC第14次正课-Ratio-Test与Taylor-Series · 13. After Class Summary / 看完压缩版
- Interval of Convergence 用 Ratio Test 先找 open interval，再 check endpoints。
- 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。