[Math] Example of a conditionally convergent series that is not alternating

Question

Every example of a conditionally convergent series I can think of is alternating. Can someone find a non-alternating conditionally convergent series? Thanks.

Answer 1

Any convergent reordering of a conditionally convergent series will be conditionally convergent. A typical example is the reordering $$ 1,-\frac12,-\frac14,\frac13,-\frac16,-\frac18,\frac15,-\frac1{10},-\frac1{12},\frac17,-\frac1{14},\ldots $$ of the alternating harmonic series, with sum $\frac12\,\log2$.