Arithmetic Series Sum Calculator — 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:
- Number of terms: floor((b - a) / d) + 1
- Sum = n/2 × (first + last)

Exemplo Resolvido

Sum all integers from 1 to 100.

  1. Number of terms = 100
  2. Sum = 100/2 × (1 + 100)
  3. = 50 × 101
  4. = 5050