Using the fact that if $P(z)=a_nz^n +···+a_1z+a_0,$ is a polynomial of degree $n$ then there is $R_0 > 0$ such that for $|z| > R_0$ the polynomial can be bounded from below as $$|P(z)|>\frac{1}{2}|a_n||z|^n$$I need to show that if $P(z)$ is polynomial of degree $n ≥ 2$ and $C_R$ is the circle of radius $R$ centered at 0 then $$\lim_{R\rightarrow \infty} \int_{C_R} \frac{1}{P(z)}dz=0$$
Any hints or help would be appreciated