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Mathematica

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  • $\begingroup$ Interesting, it seems my PrecisionGoal -> Infinty was causing some trouble. I see now that AccuracyGoal -> Infinity, PrecisionGoal -> 47 is better than AccuracyGoal -> 47, PrecisionGoal -> Infinty. $\endgroup$ Commented Jun 7, 2014 at 9:58
  • $\begingroup$ @Jean-ClaudeArbaut - It is, of course, unsatisfactory, that you only find the "correct" number for NSumTerms (approx. 10000) by trial and error. Thanks for this interesting question. $\endgroup$ Commented Jun 7, 2014 at 10:01
  • $\begingroup$ This doesn't directly answer the original question, but why not use the fact that Mathematica can evaluate the exact sum symbolically: Sum[(-1)^n/n^3, {n, 1, Infinity}] gives (-3*Zeta[3])/4. You may then use N, with a 2nd argument to specify the desired precision. $\endgroup$ Commented Jun 7, 2014 at 15:23
  • $\begingroup$ @murray - for me thats THE answer if you can evaluate symbolically. $\endgroup$ Commented Jun 7, 2014 at 15:30
  • $\begingroup$ @eldo: OK, I made my comment into an answer. $\endgroup$ Commented Jun 7, 2014 at 19:40