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Calculus Level pending

Let \(F(x) \) represent the x-th term of a sequence defined by \(F(x+1) = F(x) + F(x-1)\), where \(F(1) =1, F(2) = 2 \).

Evaluate \(\displaystyle \lim_{x \rightarrow \infty} \dfrac{F(x+10)}{F(x)+F(10)}\) to the nearest integer.

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