## example holomorphic function series

hello,
firstly i'm sorry because my english isn't well , i hope i can describe the task correctly. I have to find a holomorphic function series f_n on E:={ $z \in IC; |z| <1$ } such that f_n convergences compact to a not-constant function f, at least every function of f_n has one root on E, but f hasn't roots on E.<BR>Maybe I can take f_n(z)=z+1-1/n ?
greet, redrose5