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Topic: 1 + 2 + ... + n a polynomial how?
Replies: 5   Last Post: Apr 2, 2013 11:55 AM

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 Jussi Piitulainen Posts: 355 Registered: 12/12/04
1 + 2 + ... + n a polynomial how?
Posted: Apr 1, 2013 12:18 PM

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.

Date Subject Author
4/1/13 Jussi Piitulainen
4/1/13 dan.ms.chaos@gmail.com
4/1/13 Timothy Murphy
4/1/13 David Petry
4/2/13 David Bernier
4/2/13 David C. Ullrich