Possible Duplicate:
Prove that if $\sum a_k z_1^k$ converges, then $\sum a_k z^k$ also converges, for $|z|<|z_1|$
I have to prove that : Given a power series $\sum_n a_n x^n$ diverges for $x = x'$ then it diverges for every $x$ such that $| x | > |x'|$ . Please suggest how to proceed.
I am trying to use the First comparison test, knowing the series $\sum_n a_n x'^n$ is not convergent which implies that it is not absolutely convergent.
Then comparing the $n$'th terms of the series we have
$ | a_n x'^n | < | a_n x ^n | $
Since the series on the left is not convergent, we have that the series on the right is not convergent either.
But I am getting the not absolute convergence of the series by this approach...Please help !