Assume that f(x) is periodic with period 2pi and is given by f(x) = 0 if -pi

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Assume that f(x) is periodic with period 2pi and is given by f(x) = 0 if -pi<x<0 pi-x if 0<x<pi   (a) Show that the fourier series of f(x) is given by      2. Assume that f(x) is periodic with period 2? and is given by f(x)={0??x?ifif????x<00?x<?? (a) Show that the Fourier series of f(x) is given by f(x)?4??+n=1???(?n21?(?1)n?cos(nx)+n1?sin(nx)). [22 marks] (b) By evaluating this Fourier series at a suitable point, prove that 8?2?=1+91?+251?+491?+811?+?. Explain your reasoning. [8 marks] solutionspile.com

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