singularities and residues

Consider the function . Find its singularities and compute residues.

I know the denominator vanishes for integer. I first consider , so the function is analytic in $ , and i can write in this punctured disc the following Laurent expansion:

starting from i get Hence

thus i can write where .

So we have higther terms.

Finally, we get + higther terms, fromw which i desume that is a removable singularity for f.

But now i don't knoe hoe to deal with with . I imagine those to be all poles of order 2 for , but how to prove?

A lats question: is it correct to say: the poles accumulates to , hence is not an isolated singularity, thus i cannot compute ?