Sum of odd numbers

The sum of all positive odd numbers up to 2n − 1 is the perfect square n2

Proof 1

The first square is formed by 1 block; 1 is the first square. The next strip, made of white squares, shows how adding 3 more blocks makes another square: four. The next strip, made of black squares, shows how adding 5 more blocks makes the next square. This process can continue indefinitely.