Section10.6-Power Series

Section10.6-Power Series

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Unformatted text preview: 2 x3 x n x n 1 x n0 if x 1 What does it mean that a function is equal to a series? Substitution We find more functions with power series representations by substitution into a known function and associated power series: n 1 x2 x2n 1 x2 x4 1 x 2 n 0 n 0 Then use substitution to find interval of convergence: x2 1 x 1 More Substitution 1 1 1 2 x 1 2 x 2 x n n 0 1 n n 1 2 x 1 2 x n 0 for 2 x 1 or x 1 2 Multiplication We find more functions with power series representations by multiplying a known function and associated power series by a constant or by a power of x. This does not affect the interval of convergence. 5 1 5 5 x n 5 x n 1 x 1 x n0 n 0 x 1 x x x n x n 1 1 x 1 x n 0 n 0 for x 1 for x 1 Multiplication and Substitution 1 1 3 x x 3 1 3 1 1 3 1 x 3 1 x 3 n 0 3 1 xn n...
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This note was uploaded on 02/24/2014 for the course APMA 1110 taught by Professor Morris during the Fall '11 term at UVA.

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