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Documentation / Mathematica / Built-in Functions / Numerical Computation / Sums and Products /


FilledSmallSquare Sum[f, i, imax] evaluates the sum .

FilledSmallSquare Sum[f, i, imin, imax] starts with i = imin. Sum[f, i, imin, imax, di] uses steps di.

FilledSmallSquare Sum[f, i, imin, imax, j, jmin, jmax, ... ] evaluates the multiple sum .

FilledSmallSquare Sum[f, i, imax] can be entered as .

FilledSmallSquare can be entered as AliasIndicatorsumAliasIndicator or \[Sum].

FilledSmallSquare Sum[f, i, imin, imax] can be entered as .

FilledSmallSquare The limits should be underscripts and overscripts of in normal input, and subscripts and superscripts when embedded in other text.

FilledSmallSquare Sum evaluates its arguments in a non-standard way (see Section A.4.2).

FilledSmallSquare Sum uses the standard Mathematica iteration specification.

FilledSmallSquare The iteration variable i is treated as local.

FilledSmallSquare In multiple sums, the range of the outermost variable is given first.

FilledSmallSquare The limits of summation need not be numbers. They can be Infinity or symbolic expressions.

FilledSmallSquare If a sum cannot be carried out explicitly by adding up a finite number of terms, Sum will attempt to find a symbolic result. In this case, f is first evaluated symbolically.

FilledSmallSquare Sum can do essentially all sums that are given in standard books of tables.

FilledSmallSquare Sum is output in StandardForm using .

FilledSmallSquare See Section 1.5.4 and Section 3.6.7.

FilledSmallSquare Implementation Notes: see Section A.9.5.

FilledSmallSquare See also: Do, Product, Table, NSum, ZTransform, Total, RSolve.

FilledSmallSquare New in Version 1; modified in 3.

Further Examples