Riemann's Theorem on Rearranging Conditionally Convergent Series

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Conditionally convergent series of real numbers have the interesting property that the terms of the series can be rearranged to converge to any real value or diverge to . In this Demonstration, you can select from five conditionally convergent series and you can adjust the target value . The Demonstration rearranges the series, plots its partial sum (the sum from 0 to the term), and shows the rearranged series.

Contributed by: Victor Phan (October 2013)
Suggested by: Simon Tyler
Open content licensed under CC BY-NC-SA


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The five series without rearrangement are

,

,

,

,

,

where is Euler's constant, is the Riemann zeta function, and is the generalized Riemann zeta function.



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