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

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

Thanks!