The fact that the sum of odd numbers starting at one is always a square number, is easily explained by this image
As with many things mathematical, understanding a concept is much easier if one finds a way to visualize it.
While we see numbers and letters, perhaps mathematicians can transform them into a two or three-dimensional visual image, helping them see the answer to questions that baffle many of us.
An example of this can be seen by using this simple picture to prove that the sum of the first n odd numbers is always the square of n.
Of course you may not know that n, translated from mathematics into English, simply means "any given number".
As you can see from the illustration, if we start with one square (one being an odd number) and simply add another layer of little squares to the top and right of the existing square or squares, one effectively always adds an odd number.
If we want to know how many little squares there are in total, we follow a simple principle. We multiply the number of little squares on each side.
Not surprisingly, this results in the square of the number of layers or, in simple English, n multiplied by itself. This is how what may seem to be a difficult concept, can easily be understood by creating a picture!