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Unformatted text preview: g ( x ). By comparing graphs, note that f ( x ) =2 g ( x + ). Now using the Fourier series of g ( x ) from Example, we get f ( x ) =2 n =1 sin n ( + x ) n = 2 n =1 (1) n +1 n sin nx. 17. Setting x = in the Fourier series expansion in Exercise 9 and using the fact that the Fourier series converges for all x to f ( x ), we obtain 2 = f ( ) = 2 3 + 4 n =1 (1) n n 2 cos n = 2 3 + 4 n =1 1 n 2 , where we have used cos n = (1) n . Simplifying, we nd 2 6 = n =1 1 n 2 ....
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.
 Fall '11
 StuartChalk

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