Suppose $f(z)$ is holomorphic in a punctured disc $D_r(z_0) − \{z_0\}$. Suppose also that $|f(z)| \leq A|z − z_0| ^{−1+\epsilon}$ for some $\epsilon> 0$, and all $z$ near $z_0$. Show that the singularity of $f$ at $z_0$ is removable.