Thanks for the reply. What you are doing is not quite what I had in mind. I am looking to sum over the integers minus a finite set, not sum the integers minus a certain. Specifically, I am trying to write a procedure that will sum terms that do not have removable singularities separately from the terms that do have removable singularities.
b[n]=2*sin(Pi*n)/(Pi*(n^2-1)) (yes, this is a fourier series...)
The above coefficients over n (positive integer <= N) have a removable singularity at n=1. I would like write the fourier series as the addition of the removable terms plus the rest of the terms. In many cases, all the coefficients of terms without singularities will be zero.
I hope this clarifies things a bit.