sum
definite and indefinite symbolic summation
Calling Sequence
Parameters
Basic Information
Examples
Details
Compatibility
sum(f, k)
∑kf
sum(f, k=m..n)
∑k=mnf
f
-
expression
k
name; summation index
m, n
integers or arbitrary expressions
Description
The sum command (sum) is for symbolic summation.
You can enter the command sum using either the 1-D or 2-D calling sequence. For example, sum(k^2,k) is equivalent to ∑kk2.
Output
Computes a closed form for a sum.
Maple returns the call unevaluated if it cannot find a closed form.
Note
To add a finite sequence of values, rather than compute a formula, use the add command. For example, add(k, k=0..9) returns 45. Although the sum command can often be used to compute explicit sums, it is strongly recommended that the add command be used in programs if an explicit sum is needed, in particular, when summing over all elements of a list, Array, Matrix, or similar data structure.
Typical Examples
sumk2,k
13k3−12k2+16k
sumk,k=0..n−1
12n2−12n
sumk+1,k=0..n
1+n22+12+n2
sum1k!,k=0..∞
ⅇ
To add a finite sequence of values, the add command can be used.
sumk+1,k=0..6
28
addk+1,k=0..6
Classical Telescoping
sumbinomial2n−2k,n−k24k2k2k+1binomial2k,k−1,k=1..n
−2n−2n−1−16n+822n+1
For detailed information including:
Complete description of all parameters
Complete description of functionality including indefinite summation and the inert form, Sum
Details and examples comparing sum and add commands
see the sum/details help page.
The sum command was updated in Maple 15; see Enhancements to Computational Algorithms in Maple 15 .
The sum command was updated in Maple 2016; see Advanced Math .
See Also
add
collect
convert/StandardFunctions
evalf/Sum
expand
mul
normal
product
RootOf
SumTools
SumTools[IndefiniteSum][AddIndefiniteSum]
Download Help Document
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