State Runge's theorem about the uniform approximation of holomorphic functions by polynomials.

Explicitly construct, with a brief justification, a sequence of polynomials which converges uniformly to $1 / z$ on the semicircle $\{z:|z|=1, \operatorname{Re}(z) \leqslant 0\}$.

Does there exist a sequence of polynomials converging uniformly to $1 / z$ on $\{z:|z|=1, z \neq 1\}$ ? Give a justification.