Sequence-ception : The sequence of a sequence

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The sequence {\(u_n\)} is such that \(u_n = \frac{n(n+2)}{(n+1)^2}\), \(n \in \mathbb{Z}^+\).

Another sequence, {\(v_n\)}, is such that \(v_{n+1} = (2^{ln(u_n)})v_n\) , and \(v_1 = 4\) , \(n \in \mathbb{Z}^+\).

The value of \(\lim_{n \rightarrow \infty}v_n\) can be expressed as \(\lim_{n \rightarrow \infty}v_n = 2^{(A-Bln2)}\). What is the value of \(A + B\) ?

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