Date: Apr 1, 2013 12:18 PM Author: Jussi Piitulainen Subject: 1 + 2 + ... + n a polynomial how? 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.

Thanks for any insight.