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Sum ()

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Sum[f, {i, imax}]
evaluates the sum ∑_(i=1)^(i_(max))f.
Sum[f, {i, imin, imax}]
starts with i=i_(min).
Sum[f, {i, imin, imax, di}]
uses steps d​i.
Sum[expr, {i, {i1, i2, ...}}]
uses successive values i_1,i_2,….
Sum[f, {i, imin, imax}, {j, jmin, jmax}, ...]
evaluates the multiple sum ∑_(i=i_(min))^(i_(max))∑_(j=j_(min))^(j_(max))…f.
  • Sum[f, {i, imax}] can be entered as ∑_i^(i_(max))f.
  • ∑ can be entered as Esc sum Esc or \[Sum].
  • Sum[f, {i, imin, imax}] can be entered as ∑_(i=i_(min))^(i_(max))f.
  • 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, i is typically assigned a sequence of values, with f 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, f is first evaluated symbolically.
  • Sum can do essentially all sums that are given in standard books of tables.
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