Carl Gauss’s formula to quickly add up all numbers from 1 to n.

by AdamStanislav - uploaded on April 4, 2016, 6:08 pm

Carl Gauss’s formula to quickly add up all numbers from 1 to n. He came up with it as a school child when his math teacher wanted to keep the students busy for an hour, so he asked them to add up all the numbers from 1 to 100. Much to his surprise, young Carl told him in no time the result was 5050.



When asked how he could add up all those numbers so quickly, Carl said that 1+100=101, 2+99=101, etc, 50+51=101, therefore, the sum of all numbers from 1 to 100 was 101 multiplied by 50, which is 5050.



This graphic is the same formula, scribbled by my hand, just generalized to the sum of numbers from 1 to any number n. It is a classical example of how to solve a seemingly hard problem so easily that even a child could do it (even if not every child :).