If you sum any string of odd numbers starting at 1 is always a square number!
Even, odd, square, square root, positive negative. 1+1=2, a negative multiplied by a negative is always a positive, a square number can’t be negative.
When it comes to math, there are a lot of rules and patterns. And here’s another rule for you: the sum of the first ‘n’ odd numbers is always a square.
Think about it. 1+3=4 (a perfect square), 1+3+5=9 (another perfect square), 1+3+5+7=16 (yet another pefect square). You see where we’re going with this.
Does it apply to all sums of the first ‘n’ odd numbers though? How can we be certain? Well you can prove it by an arithmetic progression or a little induction, but do you really want to do that? We didn’t think so—take our word for it.