9860

Riemann's Theorem on Rearranging Conditionally Convergent Series

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.

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DETAILS

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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