Number Theory


Weights at the Gym and the Irrationality of Zeta(2)

Authors: Timothy W. Jones

This is an easy approach to proving zeta(2) is irrational. The reasoning is by analogy with gym weights that are rational proportions of a unit. Sometimes the sum of such weights is expressible as a multiple of a single term in the sum and sometimes it isn't. The partials of zeta(2) are of the latter type. We use a result of real analysis and this fact to show the infinite sum has this same property and hence is irrational.

Comments: 3 Pages.

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[v1] 2019-05-01 08:54:31

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