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Unformatted text preview: 21.510.50.511.52x4224y21.510.50.511.52x4224y21.510.50.511.52x4224yIn Lab4, our goal was to examine intervals of convergence of power series and the functions they represent. To do this, we took a list of various power series and evaluated them in summation notation. For example, the power series + ++* +* * …1 x x22 x33 2 x44 3 4, would be represented by the equation =!i 0kxii, where k represents the amount of terms taken from the series. This is important because the lab also called for us to graph the respective sums, with values of k between 1 and 20. For example, if k was 2, we would take the sum of the first two terms of the series (1 + x) and graph that. If k was 2, we would take the sum of the first three terms (1 + x + x22) and so on. When portraying the graphs as an animation, we see them approaching a certain equation. It is our job in the lab to figure out what equation this is and also to figure out the limits for which the power series satisfies the function for the interval of convergence is not always (∞,∞). From this, we can figure out the radius of convergence,...
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This note was uploaded on 04/07/2008 for the course MATH 172 taught by Professor Pietraho during the Spring '08 term at Bowdoin College.
 Spring '08
 Pietraho
 Calculus, Power Series

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