Question

series n=1 to n=inf

4/(n^2 - 36)

what happens when n=6 and there is 0 in the denominator? do we just skip it?

Answer 1

The singularity at n = 6 makes the series undefined. If you replace the 36 by some arbitrary parameter, p^2, then you can exactly compute the summation in terms of p. The simplest way to compute the summation is by exploiting the fact that for p = integer, you'll have a singularity. The behaviour near each singularity can be easily evaluated. This then completely determines the summation.