Number Theory

    

Validity of the Riemann Series Theorem

Authors: Fabien Sabinet

A classic example of the Riemann series theorem use the alternating harmonic series that converges to lnu2061(2) when k → ∞ and when rearranged converges now to a different value 1/2 lnu2061(2) when k → ∞. But here I demonstrate that the rearranged series always exclude terms that constitute a third series which itself converges to exactly the difference between the original series and the rearranged one and thus explains why the rearranged series do not converge toward the original value. Eventually, it demonstrates also that the theorem is certainly false.

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[v1] 2022-09-18 01:31:37

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