Counterexample: non-nilpotent formal power series with nilpotent coefficients

Hello, consider a comm. ring with 1, A. If a formal power series f\in
A[[X]] is nilpotent then its coefficients must be nilpotent. Now, what
about the converse? It appears that A cannot be Noetherian but does any
one have a counterexample for the converse?

Thanks.
Daniel Wolff

.

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