For n ≥ 3, let a regular n - sided polygon Pn be circumscribed by a circle of radius Rn and let rn be the radius of the circle inscribed in Pn. Then
\(\lim _{n \rightarrow \infty}\left(\frac{R_n}{r_n}\right)^{n^2}\)
equals
1
\(e^{\left(\pi^2\right)}\)
2
\(e^{\left(\frac{\pi^2}{2}\right)}\)
3
\(e^{\left(\frac{\pi^2}{3}\right)}\)
4
\(e^{\left(2 \pi^2\right)}\)