Is it obvious that 1 + 2 + ... + n is a polynomial of degree 2? How?
I mean the sum of the first n positive integers. I would like to see that it is a polynomial of degree 2 _without using_ the fact that it is equal to n(n + 1)/2. Zeilberger (his new Opinion 129) says Gauss could have used the polynomiality of the sum to support the equality, rather than the other way around.