Arithmetic Series Sum Calculator
Calculate the sum of an arithmetic series from 1 to n, or a custom range with a given step.
Sum Val
5,050
Formule
## 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: - Number of terms: floor((b - a) / d) + 1 - Sum = n/2 × (first + last)
Exemple Résolu
Sum all integers from 1 to 100.
- 01Number of terms = 100
- 02Sum = 100/2 × (1 + 100)
- 03= 50 × 101
- 04= 5050
Questions Fréquentes
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.
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