1. The problem statement, all variables and given/known data Give an example of a power series with [itex]R=1[\itex] that converges uniformly for [itex]|z|\le 1[\itex], but such that its derived series converges nowhere for [itex]|z=1|[\itex]. 2. Relevant equations R is the radius of convergence and the derived series is the term by term derivative. 3. The attempt at a solution I've tried a bunch of stuff but at the moment I'm leaning towards some variation of the power series for the sin function. It would be nice if there was a way to solve this without guessing and checking a bunch of times.