I am looking for an infinite convergent sum that still converges after reordering the sum but with a different limit. Are there any examples? Thanks.
different limit after reordering sum
0
$\begingroup$
real-analysis
analysis
-
2Have you heard of the [Rearrangement Theorem](http://en.wikipedia.org/wiki/Riemann_series_theorem)? – 2012-12-12
1 Answers
0
Any conditionally convergent series (i.e. convergent but not absolutely convergent) will do. A classical example is $ \sum_{n=1}^\infty\frac{(-1)^n}{n}. $