Math Help - normal convergence, meromorphic function

Let be a sequence of distinct points such that and . Show that converges normally to a meromorphic function with principal part at . (If , we replace the corresponding summand by .)


In this section, we covered the Mittag-Leffler Theorem. I am not sure if we need to apply that result here though. I am not sure what this sequence would converge to. I would appreciate some help with this. Thank you.