Problem #3177 - Math All Star

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1990

Problem - 3177

Let sequence

$\{a_n\}$ satisfy

$a_0=1$ and

$a_n=\frac{\sqrt{1+a_{n-1}^2}-1}{a_{n-1}}$ . Prove

$a_n > \frac{\pi}{2^{n+2}}$ .

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