# NSum

NSum[f,{i,imin,imax}]

gives a numerical approximation to the sum .

NSum[f,{i,imin,imax,di}]

uses a step di in the sum.

# Details and Options  • 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:
•  AccuracyGoal Infinity number of digits of final accuracy sought EvaluationMonitor None expression to evaluate whenever f is evaluated Method Automatic method to use NSumTerms 15 number of terms to use before extrapolation PrecisionGoal Automatic number of digits of final precision sought VerifyConvergence True whether to explicitly test for convergence WorkingPrecision MachinePrecision the 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 EulerMaclaurin 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.
• VerifyConvergence is only used for sums with infinite limits.
• 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.
• NSum has attribute HoldAll, and effectively uses Block to localize variables.

# Examples

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## Basic Examples(1)

Approximate an infinite sum numerically:

 In:= Out= The error versus the exact value of :

 In:= Out= ## Possible Issues(3)

Introduced in 1988
(1.0)
|
Updated in 2007
(6.0)