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Question Number 34594 by abdo mathsup 649 cc last updated on 08/May/18

prove that  Σ_(k=0) ^p (−1)^k  C_n ^k   =(−1)^p  C_(n−1) ^p

$${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{p}} \left(−\mathrm{1}\right)^{{k}} \:{C}_{{n}} ^{{k}} \:\:=\left(−\mathrm{1}\right)^{{p}} \:{C}_{{n}−\mathrm{1}} ^{{p}} \\ $$

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