Simply Nice

Calculus Level 5

\[ \xi(x) = \dfrac{\sec^{2}\left(\dfrac{x}{2}\right)}{4} \ + \ \dfrac{\sec^{2}\left(\dfrac{x}{4}\right)}{16}+ \ \dfrac{\sec^{2}\left(\dfrac{x}{8}\right)}{64} +\ ... + \dfrac{\sec^2\left( \dfrac{x}{2^n} \right)}{4^n}+ ...\]

Find no. of solutions of \(\xi(x)= 2 \) in (0,5).

HINT: Use \(trigonocalculus\).

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