MATH 141 Lecture Notes - Lecture 21: Conditional Convergence, Ibm System P, Ratio Test

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Math 141 - lecture 21 - 11. 8 power series. A power series is an infinite series that takes the form: The coefficients, , is an constant with respect to , not , such as (cid:4672)(cid:2871)(cid:2872)(cid:4673). The independent variable, , refers to the interval over which the power series converges, or the interval of convergence. The interval of convergence is denoted by . The variable, , is a constant that refers to the center of the series, or the midpoint of the interval that we find for . The distance from to either side of the interval, , is the radius of convergence, or . This is what we are ultimately looking for when working with power series. Let"s look at the first three terms of the power series: When =(cid:882), the expression (cid:4666) (cid:4667)=(cid:883), so we are just left with (cid:2868) When =(cid:883), the expression (cid:4666) (cid:4667)= , so we have (cid:2869)(cid:4666) (cid:4667)

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