An interesting story about sum of the first hundred natural numbers

 

Carl Friedrich Gauss was the German  Mathematician is known for his significant contribution in many fields of pure mathematics, like number theory, geometry, probability theory, geodesy, planetary astronomy, the theory of functions, and potential theory.

 

At school we use his form to calculate the sum of the first hundred numbers.

 Tasks of this kind were solved in a geometric way, back in ancient Greece.  Calculating the sum of the first hundred numbers using geometry.

We will show number 1 with a square, number 2 with two squares, number 3 with three squares next to each other and so on.

 

Addition 1 + 2 + 3 + ... + n  will be the arrangement of squares that in turn represent individual natural numbers in the form of an isosceles right triangle with a serrated hypotenuse.

 

In some n-th triangle in a row, we will have a total of 1 + 2 + 3 + ... + n squares and the task was reduced to deciphering that number, that is, the sum. Note that the triangle on each of the legs has n squares. Let us take two such triangles, which are congruent, and connect them along the hypotenuses:

 

We get a rectangle consisting of n (n + 1) squares, which is twice the sum of 1 + 2 + 3 + ... + n.

And so we came to the results:

 

 

Nikola PTS/Marina Nikolic/The First Technical School/Serbia