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 .