Sum

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

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

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

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

can be entered as sum or \[Sum].

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

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

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

Sum uses the standard Mathematica iteration specification.

The iteration variable i is treated as local.

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

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

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.

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

Sum is output in StandardForm using .

See Section 1.5.4 and Section 3.6.7.

Implementation Notes: see Section A.9.5.

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

New in Version 1; modified in 3.

Further Examples