Let $p(x)$ be a polynomial of degree $N$ then the radius of convergence of the power series $\sum_{n=0}^{\infty}p(n)x^n$
depends on $N$
is $1$ for all $N$
is $0$ for all $N$
is $\infty$ for all $N$
Radius of convergence $r=\lim\limits_{n\to\infty}\frac{p(n)}{p(n+1)}\rightarrow1$ ?