Question Number 210171 by hardmath last updated on 01/Aug/24
$$\mathrm{Find}: \\ $$$$\underset{\boldsymbol{\mathrm{n}}\rightarrow+\infty} {\mathrm{lim}}\:\:\frac{\mathrm{n}}{\left(\mathrm{n}!\right)^{\mathrm{2}} \:\mathrm{4}^{\boldsymbol{\mathrm{n}}} }\:\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\prod}}\:\left(\left(\mathrm{2k}−\mathrm{1}\right)^{\mathrm{2}} \:+\:\mathrm{4}\right)\:=\:? \\ $$