# Let A be a Noetherian Ring. Prove that Sum anx^n is nilpotent iff an is nilpotent.

Let $$A$$ be a Noetherian Ring. Prove that $$\sum_{n=0}^\infty a_n x^n$$ is nilpotent iff $$a_n$$ is nilpotent for all $$n\in\mathbb Z^+$$.