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algorithmsoup.wordpress.com | ||
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mikespivey.wordpress.com
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| | | | | A few months ago Mathematics Magazine published a paper of mine, "A Combinatorial View of Sums of Powers." In it I give a combinatorial interpretation for the power sum $latex \sum_{k=1}^n k^m$, together with combinatorial proofs of two formulas for this power sum. (An earlier version of some of the results in this paper actually... | |
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ckrao.wordpress.com
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| | | | | In this post I would like to prove the following identity, motivated by this tweet. $latex \displaystyle n! \prod_{k=0}^n \frac{1}{x+k} = \frac{1}{x\binom{x+n}{n}} = \sum_{k=0}^n \frac{(-1)^k \binom{n}{k}}{x+k}$ The first of these equalities is straightforward by the definition of binomial coefficients. To prove the second, we make use of partial fractions. We write the expansion $latex \displaystyle... | |
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thinking-about-science.com
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| | | | | Before you read this, I suggest you read post 16.50. In post 16.50, we saw that the effect of a force depends on its direction, as well as how big it is - force is a vector. So, if we add a force of 5 N to another force of 5 N, the result can... | |
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teachinnovatereflectblog.wordpress.com
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| | | This was my first Researched and I left with my head spinning so this is a great way of reflecting and getting ideas down on paper. It was great to listen to and meet some of the people who inspire me to be better and keep my brain ticking over constantly. I have tried to... | ||
