\(\large{A=\displaystyle \lim_{n\to \infty}(\sum^{n}_{r=0} \frac{\binom{n}{r}}{n^{r}(r+3)})}\)

Which of the following is correct

\(P)\) \(A\) is an irrational number

\(Q)\) \(lnA-2\) is rational

\(R)\) A is a rational number

\(S)\) \(log_{2} A+2\) is rational

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