Each of the numbersrepresents the number of dots that can be arranged evenly in a pentagon...

Each of the numbers

represents the number of dots that can be arranged evenly in a pentagon:

The ancient Greeks called these pentagonal numbers. If pn denotes the nth pentagonal number, where p1 = 1 and pn = pn−1 + (3n − 2) for n ≥ 2, prove that