Quote Originally Posted by problem statement
Let \sum c_nz^n have a radius of convergence R:=\sup\{|z|:\sum c_nz^n\text{ converges}\}. Prove that R=s, where

s:=\sup\{|z|:c_nz^n\to 0\text{ as }n\to\infty\}.
Of course it's easy to show that R\leq s, but I'm having problems showing that s\leq R. Any help would be much appreciated.

Thanks!