prove-that-n-N-k-0-2n-1-k-C-2n-k-2-1-n-C-2n-n-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 35037 by abdo mathsup 649 cc last updated on 14/May/18

prove that ∀ n∈N Σ_(k=0) ^(2n) (−1)^k ( C_(2n) ^k )^2 =(−1)^n C_(2n) ^n .

$${prove}\:{that}\:\forall\:{n}\in{N} \\ $$$$\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\left(−\mathrm{1}\right)^{{k}} \left(\:{C}_{\mathrm{2}{n}} ^{{k}} \right)^{\mathrm{2}} \:=\left(−\mathrm{1}\right)^{{n}} \:{C}_{\mathrm{2}{n}} ^{{n}} \:\:. \\ $$

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prove-that-n-N-k-0-2n-1-k-C-2n-k-2-1-n-C-2n-n-

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