58. Karie is inventing a new notation in math. She has decided to use n↓ to denote the sum of the first n positive integers. For example, 5↓ means 5 + 4 + 3 + 2 + 1. Karie has written 3 statements that she is investigating as possible properties of n↓ .

I. n↓+(n+1) = (n+1)↓

II. n↓+n↓ = (2n)↓

III. (n²)↓=(n↓)²

Which of these statements, if any, is (are) true for all positive integers n ?