Calcolatore Somma Serie Aritmetica
Calcola la somma dei termini di una serie aritmetica. Primo termine, ragione e numero di termini.
Sum Val
5,050
Num Terms100
Average Val50.5000
Formula
Arithmetic Series Sum
Formula (Gauss's Method)
Sum = n/2 × (first + last)
where n is the number of terms.
Famous Example
Gauss reportedly summed 1 to 100 as a child: Sum = 100/2 × (1 + 100) = 50 × 101 = 5050.
General Formula
For a series from a to b with step d:
Esempio Risolto
Sum all integers from 1 to 100.
- 01Number of terms = 100
- 02Sum = 100/2 × (1 + 100)
- 03= 50 × 101
- 04= 5050
Domande Frequenti
Who discovered this formula?
The formula is often attributed to young Carl Friedrich Gauss, who allegedly used it to quickly sum 1 to 100 as a schoolchild.
Does this work for non-integer steps?
Yes, the formula works for any arithmetic series regardless of step size, as long as the terms form a constant-difference sequence.
What is the sum of the first n odd numbers?
The sum of the first n odd numbers (1, 3, 5, ..., 2n-1) always equals n². For example, 1+3+5+7 = 16 = 4².
Impara