An example of a power series that has a radius of convergence of 3 The problem states "Give an example of a power series $\sum^{\infty}_{n=0}$a$_{n}$z$^{n}$ that has a radius of convergence of 3 and that represents an analytic function having no zeroes. I'm sorry if this is a little simplistic but I really can't think of anything and am having a hard time with this.

Take any series you are familiar with and has a finite radius of convergence $r$. Then rescale the argument to be $\dfrac{3z}r$. This multiplies all terms by $\dfrac{3^n}{r^3}$ and yields the desired radius.
