Let $(a_n)_n \in \mathbb{R}^{\mathbb{N}}$ be a sequence of reals such that the series $\sum (a_n)^2$ is convergent. Show that the radius of convergence of the power series $\sum a_n t^n$ is greater than or equal to 1.
Let $(a_n)_n \in \mathbb{R}^{\mathbb{N}}$ be a sequence of reals such that the series $\sum (a_n)^2$ is convergent.\\
Show that the radius of convergence of the power series $\sum a_n t^n$ is greater than or equal to 1.