Let \(\sum_{n=1}^{\infty} a_{n} z^{n} \) be a convergent power series such that \(\lim _{n \rightarrow \infty} \frac{a_{n+1}}{a_{n}}=R>0\). Let p be a polynomial of degree d. Then the radius of convergence of the power series \(\sum_{n=0}^{\infty} a_{n} p(n) z^{n}\) equals