Consider the following 27-periodic function: = { Note that the 27-periodicity of the above function essentially...

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Consider the following 27-periodic function: = {² Note that the 27-periodicity of the above function essentially says that f(л) := f(-) = 0. f(x): for x € [-7,0) for x = [0, π) (2a) Find the Fourier series of the above function. (2b) Employing the theorem of Dirichlet at the point x = 0 for the Fourier series obtained in Question (2a), show that sums to 1 1 1 1- + 2² 32 4² (2c) Deduce from the sum obtained in Question (2b) that the following series 1 1. 1 1 + + + 22 32 42 + 77² 12 Consider the following 27-periodic function: = {² Note that the 27-periodicity of the above function essentially says that f(л) := f(-) = 0. f(x): for x € [-7,0) for x = [0, π) (2a) Find the Fourier series of the above function. (2b) Employing the theorem of Dirichlet at the point x = 0 for the Fourier series obtained in Question (2a), show that sums to 1 1 1 1- + 2² 32 4² (2c) Deduce from the sum obtained in Question (2b) that the following series 1 1. 1 1 + + + 22 32 42 + 77² 12

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