3 ms·
What is a neat characteristics of N^2 where N is integer is that its value is the sum of the first N odd integers. 1^2 = 1 2^2 = 1 + 3 = 4 3^2 = 1 + 3 + 5 = 9
by bitL 13y ago
What is a neat characteristics of N^2 where N is integer is that its value is the sum of the first N odd integers.
1^2 = 1
2^2 = 1 + 3 = 4
3^2 = 1 + 3 + 5 = 9
4^2 = 1 + 3 + 5 + 7 = 16
...
I am wondering if there is a relation of this to the article.
- ufo 13y agoNot 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.