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Mention Faulhaber's formula

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Antti H S Laaksonen 2017-04-18 21:39:31 +03:00
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@ -525,7 +525,9 @@ Each sum of the form
where $k$ is a positive integer, where $k$ is a positive integer,
has a closed-form formula that is a has a closed-form formula that is a
polynomial of degree $k+1$. 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.},
\[\sum_{x=1}^n x = 1+2+3+\ldots+n = \frac{n(n+1)}{2}\] \[\sum_{x=1}^n x = 1+2+3+\ldots+n = \frac{n(n+1)}{2}\]
and and
\[\sum_{x=1}^n x^2 = 1^2+2^2+3^2+\ldots+n^2 = \frac{n(n+1)(2n+1)}{6}.\] \[\sum_{x=1}^n x^2 = 1^2+2^2+3^2+\ldots+n^2 = \frac{n(n+1)(2n+1)}{6}.\]