Euler-Maclaurin summation formula

[TriTertButoxy]

I am interested in knowing under what conditions the Euler-Maclaurin summation formula converges (including the remainder term). Is there anywhere in the texts or literature where they discuss this?

Thanks.

[TriTertButoxy]

Does the sum converge provided the integral converges, and vice-versa? What about the remainder terms? do they converge? I'm not too concerned with the rate of convergence; I just want to know if converges. Or where in the literature I can find the answer.

It seems to me that Euler-Maclaurin summation formula always converges.