# boundedness

## Criterion for boundedness of power series ★

Author(s): Rüdinger

\begin{question} Give a necessary and sufficient criterion for the sequence $(a_n)$ so that the power series $\sum_{n=0}^{\infty} a_n x^n$ is bounded for all $x \in \mathbb{R}$. \end{question}

Keywords: boundedness; power series; real analysis