\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
A sequence \((v_n)\) is defined by \(v_{n+1} = \dfrac{2v_n + 3}{v_n + 4}\) and is known to converge to a positive limit \(\ell\).
Determine the exact value of \(\ell\).
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