Not really. First of all, the article is about real-valued functions while your fact is only interesting for integers. Secondly, the article is about polynomial

Not really. First of all, the article is about real-valued functions while your fact is only interesting for integers. Secondly, the article is about polynomials in general, meaning that the proof still works if you multiply everything by a constant factor and add terms of a lower degree. The reason this matters is that sum(i^k for i from 1 to N) will always be a polynomial of degree (k+1) and the only special thing about your sum in this case (not having a constant factor or lower order tems) is not something tha the proof in the article cares about.