求问组合数

学术版

Dream__Sky @ 2024-10-02 13:56:17

1\times C_{k-1}^{0}+2\times C_{k-1}^{1}+\ldots n\times C^{n-1}_{k-1}

怎么算？能不能给出详细过程谢谢

by EityDawn @ 2024-10-02 14:06:12

@Dream__Sky 拆一下

kC_{n}^k=nC_{n-1}^{k-1}

by Composite_Function @ 2024-10-02 14:09:27

原式等于 \dfrac{1}{k}(\sum_{i=1}^{min(n,k)}C_{k}^{i})，然后裂项即可

by M4rkSELby @ 2024-10-02 14:11:27

@Composite_Function 请问怎么裂项？

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