Date: Oct 8, 2013 8:25 AM
Author: Peter Scales
Subject: Re: Here's a little challenge for you guys.

Hi Guy,

> Get this: every odd number that is added up to equal
> a certain number that is squared will hold true.
>
> Here it is written out:
> _________________________
>
> +1  +3  +5  +7   +9   +11
>
> 1   4   9   16   25   36
>
> 1^2 2^2 3^2 4^2  5^2  6^2
> _________________________

You asked:
> Now, I want to know why these values equal the same
> numbers (i.e. 9 = 1+3+5 = 3^2, 36 = 1+3+5+7+9+11 =
> 6^2)


For a proof without words try writing the numbers in a square array as:
13579
33579
55579
77779
99999
Taking the squares from the top left you can see that
1=1^2, 1+3=2^2, 1+3+5=3^2, 1+3+5+7=4^2, etc.

Regards, Peter Scales.