From 8916cbfdcdab70f29bf3f939e69c8fc396c24ba7 Mon Sep 17 00:00:00 2001 From: Antti H S Laaksonen Date: Tue, 18 Apr 2017 21:39:31 +0300 Subject: [PATCH] Mention Faulhaber's formula --- chapter01.tex | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/chapter01.tex b/chapter01.tex index ea03f06..e95308c 100644 --- a/chapter01.tex +++ b/chapter01.tex @@ -525,7 +525,9 @@ Each sum of the form where $k$ is a positive integer, has a closed-form formula that is a polynomial of degree $k+1$. -For example, +For example\footnote{\index{Faulhaber's formula} +There is even a general formula for such sums, called \key{Faulhaber's formula}, +but it is too complex to be presented here.}, \[\sum_{x=1}^n x = 1+2+3+\ldots+n = \frac{n(n+1)}{2}\] and \[\sum_{x=1}^n x^2 = 1^2+2^2+3^2+\ldots+n^2 = \frac{n(n+1)(2n+1)}{6}.\]