Consider the function f L2[0, 1] f(x) = { 1 x for 0 x 1/2 -x...

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Consider the function f L2[0, 1] f(x) = { 1 x for 0 x 1/2 -x for 1/2 < x < 1 An orthonormal basis in the Hilbert space L2 [0, 1] is given by B:= {1, 2 cos(x): n = 1, 2,...}. (i) Find the Fourier expansion of with respect to this orthonormal basis. (ii) From this expansion show that we can calculate 8 = k=0 1 (2k + 1) (1) Consider the function f L2[0, 1] f(x) = { 1 x for 0 x 1/2 -x for 1/2 < x < 1 An orthonormal basis in the Hilbert space L2 [0, 1] is given by B:= {1, 2 cos(x): n = 1, 2,...}. (i) Find the Fourier expansion of with respect to this orthonormal basis. (ii) From this expansion show that we can calculate 8 = k=0 1 (2k + 1) (1)