RedAssign14[1].1 - Unit Sequences and Series Module Power...

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Unit: Sequences and Series Module: Power Series Representations of Functions Differentiation and Integration of Power Series [email protected] Copyright 2001, Thinkwell Corp. All Rights Reserved. 1631 –rev 06/15/2001 You can do calculus on a power series inside its interval of convergence. The derivative of the power series = 0 () n n n axc is = 1 1 n n n na x c . The integral of the power series = 0 n n n is + = + + 1 0 1 n n n C n . Inside its interval of convergence a power series defines a function that you can differentiate and integrate. Since constant terms disappear during differentiation, you can start the index of the derivative at n =1. There are many ways to integrate a power series.
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This note was uploaded on 04/27/2010 for the course MATH 172 taught by Professor Hyon during the Spring '10 term at Community College of Denver.

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