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# EulerSum

 EulerSum[f, {i, imin, imax}]gives a numerical approximation to the sum f using Euler's transformation. EulerSum[f, {i, imin, imax, di}] uses a step di in the sum.
• EulerSum is particularly good for working with alternating series and series whose terms have the form , where is a polynomial in n.
• EulerSum can be used for sums with both finite and infinite limits.
• The following options can be given:
 EulerRatio Automatic parameter used in generalized Euler transformations ExtraTerms 7 number of terms to use during extrapolation Terms 5 number of terms to use before extrapolation WorkingPrecision MachinePrecision the precision used in internal computations
• Valid settings for EulerRatio are Automatic, a single ratio, or a list of ratios or {ratio, degree+1} pairs. In the case of a list, the various ratios are used successively in iterated Euler transformations.
• With the default setting Automatic, the value used for EulerRatio is based on the ratio of successive terms in the series.
• Valid settings for ExtraTerms are integers greater than 1. The default setting is 7.
• The setting for ExtraTerms gives the number of terms to be used in the extrapolation process after the number of terms specified by the option Terms have been explicitly summed.
• Valid settings for Terms are positive integers.