Let k be non-negative real numbers and n ∈ N^+ ≥1. Prove that (((4−k)/(4+k)))(((12−k)/(12+k)))...[((2n(n+1)−k)/(2n(n+1)+k))] ≤ ((n+k+1)/((n+1)(k+1)))


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Question Number 142710 by loveineq last updated on 04/Jun/21

$Let k be non - negative real numbers and n \in N^{+} ⩾ 1 .$ $Prove that$ $(\frac{4 - k}{4 + k}) (\frac{12 - k}{12 + k}) . . . [\frac{2 n (n + 1) - k}{2 n (n + 1) + k}] ⩽ \frac{n + k + 1}{(n + 1) (k + 1)}$
	Answered by loveineq last updated on 06/Jun/21

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