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Question Number 194140 by MM42 last updated on 28/Jun/23

prove it : ((n),(k) )^( 2) ≥ ((( n)),((k−1)) ) × ((( n)),((k+1)) ) ; 1≤k≤n−1

proveit:(nk)2⩾(nk−1)×(nk+1);1⩽k⩽n−1

Answered by witcher3 last updated on 28/Jun/23

(((n!)/(k!.(n−k)!)))^2 ≥((n!)/((n−k+1)!.(k−1)!)).((n!)/((k+1)!.(n−k−1)!)) ⇔((n−k)/k).((k+1)/((n−k)))≥1⇔((k+1)/k)≥1 True

(n!k!.(n−k)!)2⩾n!(n−k+1)!.(k−1)!.n!(k+1)!.(n−k−1)!⇔n−kk.k+1(n−k)⩾1⇔k+1k⩾1True

Commented by York12 last updated on 28/Jun/23

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