Soma 1+2+…+n

The sum of the first n natural numbers calculator quickly computes 1+2+3+...+n using Gauss's famous formula: S = n(n+1)/2. Simply enter n and get the result instantly. Ideal for students, teachers, and professionals who need to compute sequential sums without adding term by term.

The formula was discovered by Carl Friedrich Gauss in his childhood when he realized that the sum of an arithmetic progression can be simplified. The method multiplies the number of terms (n) by the sum of the first and last term (n+1) and divides by two. This works because the sum is symmetric: 1+n, 2+(n-1), etc., all yield the same value.

Use this calculator for situations like calculating the total number of items in a sequence, estimating the number of handshakes in a group (n*(n-1)/2), or checking basic math exercises. It is also useful in programming to test summation algorithms. The tool is free and requires no registration.

Caution: the formula only works for natural numbers (1,2,3,...). Ensure n is a positive integer. For sequences that do not start at 1, the formula needs adjustment. Also, the calculator does not handle partial sums or different intervals; it assumes the sum starts at 1 and ends at n.