show-that-C-n-k-C-n-1-k-1-C-n-2-k-1-C-k-k-1-C-k-1-k-1-

Tinku Tara June 4, 2023 None 0 Comments

Question Number 129642 by SOMEDAVONG last updated on 17/Jan/21

show that C_n ^k =C_(n−1) ^(k−1) +C_(n−2) ^(k−1) +....+C_k ^(k−1) +C_(k−1) ^(k−1) .

$$\mathrm{show}\:\mathrm{that}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} =\mathrm{C}_{\mathrm{n}−\mathrm{1}} ^{\mathrm{k}−\mathrm{1}} +\mathrm{C}_{\mathrm{n}−\mathrm{2}} ^{\mathrm{k}−\mathrm{1}} +….+\mathrm{C}_{\mathrm{k}} ^{\mathrm{k}−\mathrm{1}} +\mathrm{C}_{\mathrm{k}−\mathrm{1}} ^{\mathrm{k}−\mathrm{1}} . \\ $$

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