Solution
= Solution
The <radius of convergence> of a <power series> $\sum_{n\ge0}a_nz^n$ is the unique $R\in[0,\infty]$ for which the series converges absolutely when $|z|<R$ and diverges when $|z|>R$. When $R=\infty$ it converges for every complex $z$; when $R=0$ it converges only at the centre. The definition makes no assertion about convergence on $|z|=R$, so boundary points must be checked separately.