Solution
= Solution
For $z\ne0$, the ratio of successive absolute terms is
$$
\frac{|z^{n+1}|/(n+1)^2}{|z^n|/n^2}
=|z|\left(\frac n{n+1}\right)^2\longrightarrow|z|.
$$
The <ratio test> therefore gives <absolute convergence> for $|z|<1$ and divergence for $|z|>1$, while at zero the series is trivially convergent. Hence $R=1$. On the boundary, $|z^n/n^2|=1/n^2$, and the convergent <p-series> proves
$$
\boxed{R=1;\quad\text{absolute convergence at every point of }|z|=1.}
$$