Calculatrice de Sommation Gratuite
Calculez la somme d'une série mathématique (sigma). Évaluez la sommation d'une expression pour un intervalle donné.
Requested
385
Sum Integers55
Sum Squares385
Sum Cubes3,025
Formule
Summation Formulas
Sum of Integers
sum(i, 1, n) = n(n+1)/2
Sum of Squares
sum(i², 1, n) = n(n+1)(2n+1)/6
Sum of Cubes
sum(i³, 1, n) = [n(n+1)/2]²
Notice that the sum of cubes equals the square of the sum of integers.
Exemple Résolu
Sum of i² from 1 to 10.
- 01Sum of integers: 10×11/2 = 55
- 02Sum of squares: 10×11×21/6 = 2310/6 = 385
- 03Sum of cubes: (55)² = 3025
Questions Fréquentes
What is a summation?
A summation (denoted by the sigma symbol) adds up a sequence of terms following a pattern. For example, sum from i=1 to 5 of i² = 1+4+9+16+25 = 55.
Why does the sum of cubes equal the square of the sum?
This is a beautiful identity: 1³+2³+...+n³ = (1+2+...+n)². It can be proven algebraically by induction or geometrically by arranging squares.
Are there formulas for higher powers?
Yes, Faulhaber's formulas give closed-form expressions for the sum of any fixed power k. However, they become increasingly complex for larger k.
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