Question Number 154710 by mathdanisur last updated on 20/Sep/21
$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} }{\:\sqrt[{\boldsymbol{\mathrm{n}}+\mathrm{1}}]{\mathrm{2}\left(\mathrm{n}+\mathrm{1}\right)!}}\:-\:\frac{\mathrm{n}^{\mathrm{2}} }{\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{2n}!}}\right)\:=\:? \\ $$