So for example if f(x) is 1/x^2 and we look at the area around x=3:
Let's look at when n = 10:
So we can find expressions like this for n = 20:
which says that 1/x^3 or zeta(3) should be roughly equal to 1.217707604... summed to infinity via these Ci functions which are equal to:
Unfornutaely I don't know exactly how maple figures these integrals as n gets larger but it looks like there will be a way to write a generalized sum for any n.