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
(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?