Number Theory

    

New Proof that the Sum of Natural Number is 1/12 of Zeta Function

Authors: K. Sugiyama

   We prove that the sum of natural numbers is -1/12 of the value of the zeta function by the new method.

   Abel calculated the sum of the divergent series by the Abel summation method. However, we cannot calculate the sum of natural numbers by the method. In this paper, we calculate the sum of the natural numbers by the extended Abel summation method.

Comments: 36 Pages.

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Submission history

[v1] 2014-04-16 08:17:13
[v2] 2014-04-17 12:12:04 (removed)
[v3] 2014-04-18 17:39:32 (removed)
[v4] 2014-04-21 08:12:42 (removed)
[v5] 2014-04-22 06:38:02 (removed)
[v6] 2014-04-24 06:52:17 (removed)
[v7] 2014-04-26 07:16:03 (removed)
[v8] 2014-04-27 06:42:27 (removed)
[v9] 2014-05-22 07:24:03 (removed)
[vA] 2014-06-29 08:50:30 (removed)
[vB] 2014-10-27 03:46:36 (removed)
[vC] 2015-02-15 08:30:19
[vD] 2016-07-09 04:01:12

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