Proving ∑ 1/(n^2) = (Pi^2)/6 using Cauchy's Residue Theorem - 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.
Residues - Please see the attached file for the fully formatted problems.
Quadratic Congruences - Use Quadratic Congruences to evaluate the following fractions. See attached file for full problem description.