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Question

Real Analysis Question on Sequences and Series

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→∞(Rnrn)n2\lim\limits_{n \rightarrow \infin}(\frac{R_n}{r_n})^{n^2}
equals

A

e(π2)e^{(\pi^2)}

B

e(π22)e^{(\frac{\pi^2}{2})}

C

e(π23)e^{(\frac{\pi^2}{3})}

D

e2π2e^{2\pi^2}

Answer

e(π22)e^{(\frac{\pi^2}{2})}

Explanation

Solution

The correct option is (B) : e(π22)e^{(\frac{\pi^2}{2})}.