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[组合] 将集合$\{1,2,3,\cdots,19\}$中每两个互异的数相乘求其和

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isee posted 2021-10-2 16:26 |Read mode
将集合$\{x\in \mathrm Z\big|1\leqslant x\leqslant 19\}$中每两个互异的数相乘,求所有这种乘积的和.










































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kuing posted 2021-10-2 17:13
key: \[\sum_{1\leqslant i<j\leqslant n}x_ix_j=\frac12\left(\left(\sum_{i=1}^nx_i\right)^2-\sum_{i=1}^nx_i^2\right)\]

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