Casorati--Weierstrass for accumulating poles

Let f be analytic in \(\Omega : 0 < | z - a | < r\)except at a sequence of poles\(a _ { n } \in \Omega\)with\(\operatorname* { l i m } _ { n \to \infty } a _ { n } = a\). Show that for any w\(\in \mathbb { C }\), there exists a sequence\(z _ { n } \in \Omega\)such that\(\operatorname* { l i m } _ { n \to \infty } f ( z _ { n } ) = w\)

Explain the similarity and difference between the above assertion and the Weierstrass-Casorati theorem.