What is the sum of the first 100 positive integers?

To find the sum of the first 100 integers, you first add 1 plus 100 (the first and last numbers of the set) and get 101. Do the same with the next two integers, 2 and 99 and you'll get 101. Since you are adding two integers at a time and there are 100 integers between 1 and 100, you'll get 101, fifty times.
Therefore, a shortcut would be to simply multiply 101 times 50 and get 5,050.