KVPY #19

Geometry Level 3

Let 0<θ<π2 0 <\theta < \dfrac \pi 2 satisfying tan⁡θ=32 \tan \theta = \sqrt{ \dfrac 32 } . Evaluate

1+2(1−cos⁡θ)+3(1−cos⁡θ)2+⋯ . 1 + 2(1-\cos \theta) + 3(1-\cos \theta)^2 + \cdots .

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Rahil Sehgal by Rahil Sehgal
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