I am confronted with the following problem:
The radius of convergence of a function $f(z)=\sum c_n(z-z_0)^n$ is $R$, and the function has a pole at some $w_0$, with $|w_0-z_0|=R$. Why does, for any other $w$ on the circle with radius $R$, the series not converge absolutely?
I tried to use the MVT, but that does not work out. Can anyone give me a sketch of the proof?