Strange NSum behavior for slightly larger number of terms

Question

For some sums, NSum gives me the result nicely for some number of terms, but if I add one more term, it suddenly becomes much slower. I haven't found the minimum example for which this can be reproduced, but here is a problem I was just trying to compute:

NSum[Sin[x0*n*Pi]*Sin[d*n*Pi/2]*Exp[(n*Pi)^2 *t]*(2 - Cos[n*Pi] - 
2*BesselJ[1, n*Pi/2]*Sin[n*Pi/2]), {n, 1, 24}]

Here t=-0.3, d=0.1 and x0=0.5. For 24 terms, this evaluates just fine (and gives me 0.015118), but for 25 terms, the calculation takes much longer. It seems to me that adding just one more term to the sum should not take much longer than the original calculation. What is going on here? I'm using Mathematica version 9.0.1.0.

Answer 1

Way 1

t = -0.3; d = 0.1 ; x0 = 0.5;
NSum[Sin[x0*n*Pi]*Sin[d*n*Pi/2]*
  Exp[(n*Pi)^2*t]*(2 - Cos[n*Pi] - 2*BesselJ[1, n*Pi/2]*Sin[n*Pi/2]), {n, 1, 100}, 
  Method -> "WynnEpsilon"(*or AlternatingSigns*)]

NSum will use some algorithm.The default settings of the option Method is Automatica.But Automatica is not have better performance in any case,so we need to change this option.

Way 2

t = -0.3; d = 0.1 ; x0 = 0.5;
Sum[Sin[x0*n*Pi]*Sin[d*n*Pi/2]*
 Exp[(n*Pi)^2*t]*(2 - Cos[n*Pi] - 2*BesselJ[1, n*Pi/2]*Sin[n*Pi/2]), {n, 1, 100}]