>>10896501Subtract 1 from both odd numbers to make them even. Add up both 1s you subtracted to get 2, an even number, then add all the even numbers, which yields an even number.
Otherwise, consider all number as Mod(2). Even numbers are 0, odd numbers 1. 1 plus 1 makes 0, so adding up any two odd numbers returns an even one. In this way, it behaves analogous to multiplication of integers, where two negatives result in a positive number.
