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Consider a triangle with vertices (O, O), (1, 0), and (1, 1). For n 2 1 let Pn denote the point 1 (1,1 2) A

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Consider a triangle with vertices (O, O), (1, 0), and (1, 1). For n 2 1 let Pn denote the point 1 (1,1 2\") A small insect begins at (0, 0) and walks directly P1. It then walks directly left until it hits the hypotenuse of the triangle. It then walks directly to P2. It then walks directly left until it hits the hypotenuse of the triangle. This process repeats innitely many times: for each k, the insect walks from Pk directly left until it hits the hypotenuse, and then walks directly to Pk\". What is the total distance walked by the insect

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