Number Theory

   

A Simple Proof that Zeta(n>=2) is Irrational

Authors: Timothy W. Jones

We prove that partial sums of zeta(n>=2) are not given by any single decimal in a number base given by a denominator of their terms. This result, applied to all partials, shows that partials are excluded from an ever greater number of rational values. The limit of the partials is zeta(n) and the limit of the exclusions leaves only irrational numbers.

Comments: 5 Pages. Proofs are added for two results used in earlier drafts.

Download: PDF

Submission history

[v1] 2018-01-12 09:11:07
[v2] 2018-01-13 09:51:26
[v3] 2018-01-14 03:44:54
[v4] 2018-01-15 09:33:09
[v5] 2018-01-18 15:58:09
[v6] 2018-02-13 07:03:38

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