Solution
= Solution
The original PDF has coefficient $c_n=n^{\,n^{1/3}}$. Its $n$th root is
$$
|c_n|^{1/n}=n^{n^{-2/3}}
=\exp\!\left(\frac{\log n}{n^{2/3}}\right)\longrightarrow1.
$$
The <Cauchy-Hadamard theorem> therefore gives \b[$\boxed{R=1}$]. Again the <power series> converges absolutely inside the unit circle, while on that circle its terms do not tend to zero. The converted TeX loses the outer exponent and writes $n^{1/3}$; the calculation here uses the printed coefficient.