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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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Registered: 3/1/08
Re: 1 + 2 + ... + n a polynomial how?
Posted: Apr 1, 2013 12:42 PM
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On Apr 1, 7:18 pm, Jussi Piitulainen <>
> 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 .

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