MATH-M 212 Lecture Notes - Lecture 18: Ratio Test, Absolute Convergence
Document Summary
If a series is expanded infinitely, it is exact. 11-12-14: power series- infinite series of of the form, power series centered at - general form of a power series; is a constant, can be thought of as function. Domain- every set of -values where series converges (every power series converges at its center) Theorem 9. 20- convergence of a power series: for a power series centered at , precisely one of the following is true: There exists a real number such that the series converges absolutely for , and diverges for. The series converges absolutely for all: number is radius of convergence of the power series. If series converges at , the radius of convergence is. If series converges for all , the radius of convergence is: interval of convergence- set of all values of for which power series converges. Found by ratio test- limit does not reduce to a constant ( and )
