Matematické Fórum

stuart clark

Let $S = \{1,2,3,4,5,\cdots ,n\}.$ If $X$ denotes the set of all subsets of $S$ containing exactly two elements ,

Then the value of $\sum_{A\in X}(\min A)$ is

byk7 · 22. 10. 2018 22:19

This one is not hard, since
$\sum_{A\in X}(\min A)&=(n-1)\cdot1+(n-2)\cdot2+(n-3)\cdot3+\cdots+1\cdot(n-1)=\sum_{k=1}^{n-1}(n-k)k= \\ &=n\cdot\frac{(n-1)n}{2}-\frac{(n-1)n(2n-1)}{6}$

stuart clark · 27. 10. 2018 12:05

Thanks ↑ byk7:.

Matematické Fórum

#1 22. 10. 2018 16:55 — Editoval stuart clark (22. 10. 2018 16:55)

sum of elements in a set

#2 22. 10. 2018 22:19

Re: sum of elements in a set

#3 27. 10. 2018 12:05

Re: sum of elements in a set

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