prove that lim_(n→∞) [((((n+1)!∙(2n+1)!!))^(1/(n+1)) /(n+1))−(((n!∙(2n−1)!!))^(1/n) /n)]=(2/e^2 )


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Question Number 182646 by mathlove last updated on 12/Dec/22

$p r o v e t h a t$ $\lim_{n \to \infty} [\frac{\sqrt[n + 1]{(n + 1)! \cdot (2 n + 1)!!}}{n + 1} - \frac{\sqrt[n]{n! \cdot (2 n - 1)!!}}{n}] = \frac{2}{e^{2}}$
Commented by mathlove last updated on 13/Dec/22

$? ? ?$
Commented by mathlove last updated on 13/Dec/22

$p r o v e t h a t$ $\lim_{n \to \infty} [\frac{\sqrt[n + 1]{(n + 1)! \cdot (2 n + 1)!!}}{n + 1} - \frac{\sqrt[n]{n! \cdot (2 n - 1)!!}}{n}] = \frac{2}{e^{2}}$
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