suivant: Riemann sum : sum_riemann monter: Integration précédent: Antiderivative and definite integral   Table des matières   Index

## Discrete summation: sum

sum takes two or four arguments :
• four arguments
an expression, the name of the variable (for example n), and the bounds (for example a and b).
sum returns the discrete sum of this expression with respect to the variable from a to b.
Input :
sum(1,k,-2,n)
Output :
n+1+2
Input :
normal(sum(2*k-1,k,1,n))
Output :
n^2
Input :
sum(1/(n^2),n,1,10)
Output :
1968329/1270080
Input :
sum(1/(n^2),n,1,+(infinity))
Output :
pi^2/6
Input :
sum(1/(n^3-n),n,2,10)
Output :
27/110
Input :
sum(1/(n^3-n),n,1,+(infinity))
Output :
1/4
This result comes from the decomposition of .
Input :
partfrac(1/(n^3-n))
Output :
1/(2*(n+1))-1/n+1/(2*(n-1))
Hence :
- = - = - - -
* = *() = *(1 + + )
* = *( + + )
After simplification by , it remains :
- + *(1 + ) - + *( + ) = -
Therefore :
• for N = 10 the sum is equal to : 1/4 - 1/220 = 27/110
• for N = + the sum is equal to : 1/4 because approaches zero when N approaches infinity.

• two arguments
an expression of one variable (for example f) and the name of this variable (for example x).
sum returns the discrete antiderivative of this expression, i.e. an expression G such that G| x=n+1 - G| x=n = f| x=n.
Input :
sum(1/(x*(x+1)),x)
Output :
-1/x

suivant: Riemann sum : sum_riemann monter: Integration précédent: Antiderivative and definite integral   Table des matières   Index
giac documentation written by Renée De Graeve and Bernard Parisse