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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
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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.

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