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Find-lim-n-n-n-2-4-n-k-1-n-2k-1-2-4-




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

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