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"Making Beautiful Music in the Mathematics Classroom" Part II     by Matt DeLong

We’ve looked at this famous sum in a first-year course for mathematics majors called Problem Solving. After it was shown by the Bernoulli brothers (and others) that the harmonic series diverges, mathematicians considered this similar sum. It was known by the Bernoulli brothers that it converged, but until Euler nobody knew to what. In addition, to the sheer cleverness of Euler’s argument, this result is beautiful because of the surprise that the sum of the reciprocals of the squares adds to a number involving the most “round” of numbers, pi.

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