Arithmetische-Reihe-Rechner — Formel

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)

    • Lösungsbeispiel

    Sum all integers from 1 to 100.

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