Hint If , then and has degree less or equal than .
Edited: Of course "less" instead of "less or equal".
Let p be a polynomial of degree k>0. Prove that has radius of convergence 1 and that there exists a polynomial q(z) of degree k such that for .
I have proven the first part using the ratio test easily enough. For the second part I wrote and tried to expand the sum but didn't get anywhere productive. Can anyone help?