By the way, the proof for my previous post is as follows:

The statement “The difference between two consecutive squares” can be represented as:

(n + 1)2 - n2

…and the statement “is the sum of the two numbers being squared” can be represented as:

= (n + 1) + n; or = 2n + 1

So:

(n + 1)2 - n2 = 2n + 1

First, let’s get the square out of the first term:

(n + 1)(n + 1) - n2 = 2n + 1

Now we factor:

n2 + 2n + 1 - n2 = 2n + 1

Cancel out the n2 due to the -n2 and you get:

2n + 1 = 2n + 1.