TITLE: Is it possible for a power series to be conditionally convergent at two different points?
QUESTION [6 upvotes]: Like I stated in the title, I was just wondering if it's possible for a power series to be conditionally convergent at two different points. Are there any examples of power series that fit this criteria?
Any help is appreciated!

REPLY [2 votes]: If the argument is complex, the answer is yes.  For example $\sum\limits_{k=0}^\infty \frac{z^k}{k}$ has a radius of convergence $r=1$ and diverges for $z=1$, but converges for $z=-1$ and $z=\pm i$.
Wild guess: it converges for all points on the unit circle, except $z=1$