Radius & Interval of Convergence

AP Calculus · Axiom Academy

Lesson Radius & Interval of Convergence Finding exactly where a power series converges Use Ratio or Root Test to find R The series converges on (a-R, a+R) for sure Check each endpoint individually (plug in and test with another convergence test) : Ratio test gives |x| < 1 , so R = 1 . At x = 1 : diverges (harmonic). At x = -1 : converges (alternating harmonic). Interval of convergence: [-1, 1) . Always check endpoints — they can go either way At endpoints, use AST, p-series, or comparison tests The interval may be open, half-open, or closed

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