This is documentation for Mathematica 3, 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 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. In[1]:= Out[1]= Here is an exact sum. In[2]:= Out[2]= This makes the iterator increment in steps of 2. In[3]:= Out[3]= Here is a multiple sum. The outermost sum over i is given first, just as in standard mathematical notation. In[4]:= Out[4]= Mathematica gives an exact result for this sum. In[5]:= Out[5]= Wrapping N around this result gives a numerical approximation. In[6]:= Out[6]= You can also obtain symbolic results with Sum. In[7]:= Out[7]= In[8]:= Out[8]= In[9]:= Out[9]=