Lesson 26a - Power Series

Intervalofconvergence

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Unformatted text preview: se them to solve tougher questions! Radius/Interval of Convergence When we have a power series, we need to know which x‐values we can substitute into the infinite series and still have a convergent series. Interval of Convergence: The interval of convergence is the set of x‐values that can be substituted into the power series, and the series will converge. Radius of Convergence: The radius of convergence is half of the length of the interval of convergence (similar to that of a circle). Centre: The centre of the radius will always be “a” in our definition of a power series: an ( x a ) n a0 a1 ( x a ) a2 ( x a ) 2 a3 ( x a ) 3 ... n 0 Typically, we try to choose a=0, as it makes the series look nicer, but this is not always possible. Finding the Radius an x n Let us consider when a = 0, we get the following series n 0 Which series test should we use to determine when this series converges/diverges? We see an exponential equation (xn), but we are not too sure what an is. In any case, we know one of two tests that helps us deal w...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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