A Graphical proof for a change !

Add one to three and you get four

To that, add five and keep the score

Now isn't nine a perfect square ?

And so is four, if we are to be fair!

How do we prove that it works for n?

In a way that's simple and easy to pen ?

To be more pedantic, prove that the sum of the first 'n' odd  numbers is n squared . There are a variety of ways to do this - You could identify the Arithmetic Progression, and plug in the formula or you could use induction. Anyway, I remember stumbling upon a very elegant graphical solution to this ! It's taken me a ten minute struggle with powerpoint ( I don't know why the latest one provides so many options !) but I think it's worth it. Each time you introduce a new odd number, it fits in neatly into the picture to result in a square of bigger size !