The question can be stated in general terms as follows: “For a natural number t, what formula expresses the sum Σk = 1 + 2 + 3 + … + n as a function of n?” We present one approach to investigating such sums using methods accessible to high school and college teachers and their students. (Throughout, summations denoted Σf(k) will be assumed to run as k goes from 1 to n.)