Discussion on question by Dreamworld2001: When does the power series $\sum_{n=1}^\infty a_nx^n$ have infinitely many zeros in $(0,1)$?

Imported from a comment discussion on https://math.stackexchange.com/questions/4664083/when-does-the-power-series-sum-n-1-infty-a-nxn-have-infinitely-many-zeros