Solution
= Solution
For the <power series> coefficient $c_n=n^2$, the <Cauchy-Hadamard theorem> gives
$$
R^{-1}=\limsup_{n\to\infty}|c_n|^{1/n}
=\lim_{n\to\infty}\exp\!\left(\frac{2\log n}{n}\right)=1.
$$
Thus the \b[<radius of convergence> is $\boxed{R=1}$]. The <power series> converges absolutely for $|z|<1$ and diverges for $|z|>1$. On $|z|=1$ its terms have modulus $n^2$, so they do not tend to zero and the series diverges there as well.