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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 the Mathematica book: Section 1.5.4,¬†Section 3.6.7.
  • See also Implementation NotesA.9.55.15MainBookLinkOldButtonDataA.9.55.15.
  • See also: Do, Product, Table, NSum.

    Further Examples

    Here is the sum of the first 12 odd integers.

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    Here is an exact sum.

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    This makes the iterator increment in steps of 2.

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    Here is a multiple sum. The outermost sum over i is given first, just as in standard mathematical notation.

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    Mathematica gives an exact result for this sum.

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    Wrapping N around this result gives a numerical approximation.

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    You can also obtain symbolic results with Sum.

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