# Sequence-ception : The sequence of a sequence

Level pending

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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