Behavior of power series on the circle of convergence

Question

Is there a power series which is conditional convergent everywhere on the circle of convergence?

I know that a power serier is absolutly convergent at one point of its circle of convergence if and only if it is absolutly convergent everywhere on the circle of convergence.
So if a power serier is conditional convergent at one point of its circle of convergence, then it could not absolutly convergent at any point of its circle of convergence.

Answer 1

Another example: $\sum_{n=1}^\infty\frac{\sin n}{n}z^n$