Odd Number Theorem

The sum of the first $n$ Odd Numbers is a Square Number:

$$\sum_{k=1}^n (2k-1) = 2\sum_{k=1}^n k-\sum_{k=1}^n 1 = 2 \left[{n(n+1)\over 2}\right]-n$$

$$= n(n+1)-n=n^2.$$

See also Nicomachus's Theorem