### The formula for the sum of squares

Date: 23 Mar 2020 - Sezione: scienze/matematica/

The present essay is dedicated to the English-speaking friends. It is an answer to the question: “What is the formula for the sum of squares?” The question is ill-worded, and I assumed that it meant: “What is the the sum of the squares of the natural numbers from 1 to n?” On such assumption, I wrote an essay in two parts. The first part gives what I think to be the most elementary approach to finding the formula; the second part I give an intuitive manner to get to the same result, a child’s play with small cubes. In the first part I go into some details to explain a few elementary concepts, which are generally not underlined when (and if) the formula is discussed. For example I try to show why the formula is a third degree polynomial with constant term equal to zero. If one wants a more detailed explanation of a general formula for all sums of all powers of natural numbers from 1 to n, I suggest to have a look, for example, at http://dainoequinoziale.it/resources/scienze/matematica/sommacubi.pdf and use Google Translate if you are not familiar with the Italian language.

NOTE for the User. As with all other files, I recommend clicking on the Acrobat icon located immediately above the box of the file you have chosen, on the left. It allows you to have the entire post in a single .pdf file (no pages to turn over). Thus, the appearance of the file (text, drawings etc.) can also be enlarged with the means made available by Acrobat. Textual searches are also possible. Finally, in this form the file can be conveniently downloaded.

/