Date: Apr 1, 2013 12:42 PM
Author: dan.ms.chaos@gmail.com
Subject: Re: 1 + 2 + ... + n a polynomial how?
On Apr 1, 7:18 pm, Jussi Piitulainen <jpiit...@ling.helsinki.fi>

wrote:

> 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.

The difference between two consecutive terms of the sum series , S(n)

- S(n-1) = n , a first degree polynomial . Ergo, the sum itself is a

second degree polynomial .