10. (a) Find the Fourier series for the function ƒ: R → R determined by ƒ(x): x² for x = [−π, π] and ƒ(x + 2π) = f(x) for all x = R and using facts considered in lecture, explain why the Fourier series coverges to f(x) at each point x = (-π, πT). = (b) Using the Fourier series representation from part (a), evaluate ∞ (−1)n n² n=1

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