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NSum

NSum[f, {i, imin, imax}]
gives a numerical approximation to the sum f.
NSum[f, {i, imin, imax, di}]
uses a step di in the sum.
  • NSum can be used for sums with both finite and infinite limits.
  • NSum[f, {i, ...}, {j, ...}, ...] can be used to evaluate multidimensional sums.
  • The following options can be given:
AccuracyGoalInfinitynumber of digits of final accuracy sought
EvaluationMonitorNoneexpression to evaluate whenever f is evaluated
MethodAutomaticmethod to use
NSumTerms15number of terms to use before extrapolation
PrecisionGoalAutomaticnumber of digits of final precision sought
VerifyConvergenceTruewhether to explicitly test for convergence
WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • Possible settings for the Method option include:
"AlternatingSigns"method for summands with alternating signs
"EulerMaclaurin"Euler-Maclaurin summation method
"WynnEpsilon"Wynn epsilon extrapolation method
  • With the Euler-Maclaurin method, the options AccuracyGoal and PrecisionGoal can be used to specify the accuracy and precision to try and get in the final answer. NSum stops when the error estimates it gets imply that either the accuracy or precision sought has been reached.
  • You should realize that with sufficiently pathological summands, the algorithms used by NSum can give wrong answers. In most cases, you can test the answer by looking at its sensitivity to changes in the setting of options for NSum.
  • N[Sum[...]] calls NSum for sums that cannot be done symbolically.
  • NSum first localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically.
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