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
Snapshots
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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