This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

Sum ()

 Sum[f, {i, imax}]evaluates the sum . Sum[f, {i, imin, imax}]starts with . Sum[f, {i, imin, imax, di}]uses steps . Sum[expr, {i, {i1, i2, ...}}] uses successive values . Sum[f, {i, imin, imax}, {j, jmin, jmax}, ...]evaluates the multiple sum .
• Sum[f, {i, imax}] can be entered as .
• can be entered as Esc sum Esc 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 uses the standard Mathematica iteration specification.
• The iteration variable i is treated as local, effectively using Block.
• If the range of a sum is finite, is typically assigned a sequence of values, with being evaluated for each one.
• 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, is first evaluated symbolically.
• Sum can do essentially all sums that are given in standard books of tables.
Numeric sum:
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Symbolic sum:
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Use Esc sum Esc to enter and Ctrl+_ to enter the lower limit, then Ctrl+% for the upper limit:
 Out[1]=

Infinite sum:
 Out[1]=

Multiple sum with summation over m performed first:
 Out[1]=
 Scope   (11)
 Applications   (2)