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Proving ∑ 1/(n^2) = (Pi^2)/6 using Cauchy's Residue Theorem

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Deducing that ∑ 1/(n^2) = (Pi^2)/6 is a classic problem in Mathematics. Often it is demonstrated by using Fourier series, but it can also be proved by using Cauchy's Residue Theorem.

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∑ 1/(n^2) = (Pi^2)/6 is proven using Cauchy's Residue Theorem. The solution is detailed and well presented.

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f(z) = Pi/(z^2) * cot(Pi*z) is analytic except at z = n and z = 0.

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