Squares and Odd Numbers
Add up odd numbers from 1 onwards and you get square numbers!
 1 is a square number (= 1 × 1)
 1 + 3 = 4, and 4 is a square number (= 2 × 2)
 1 + 3 + 5 = 9, and 9 is a square number (= 3 × 3)
 etc!
Like this:
Odd Number 
Running Total 


1  1  = 1 × 1 
3  4  = 2 × 2 
5  9  = 3 ×3 
7  16  = 4 × 4 
9  25  = 5 × 5 
11  36  = 6 × 6 
etc... 
Is this some kind of magic?
Not really, just look at this picture:
 1 is a square (a 1×1 square)
 Add 3 and you get a 2×2 square
 Add 5 and you get a 3×3 square
 etc
It is good to know this, as it may help you solve things one day.
There are more such tricks, see Partial Sums.