i need to prove that the in point z=0

its loren series has endless values(i dont know the proper english term)

and their presented solution

http://i48.tinypic.com/1zb7401.jpg

(click on the photo to enlarge)

i thought of just breaking the function into a series

and it will have endless members of z in negative power.

i know that they are trying to prove that we get different limit values

so there is no limit which is a sign of that type of point

but there is no limits in their solution

i cant see limits and their results

what is it?