The sum of the first 100 odd numbers is 10,000. There are 100 odd numbers between 1 and 199, and each pair from the start and end of the sequence (e.g. 1 and 199, 3 and 197, etc.) adds up to 200. Multiplying 50 times 200 equals 10,000.
Odd numbers are defined by their parity, which is the property that makes every integer either even or odd. All odd numbers have a parity of 1, while all even numbers have a parity of 2. Any set of odd numbers can be found by using odd = {2k + 1 : k therefore Z}.
