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The line x+ y = 1 meets X-axis at A and...

The line `x+ y = 1` meets X-axis at A and Y-axis at B,P is the mid-point of `AB, P_1` is the foot ofperpendicular from P to `OA, M_1`, is that of `P_1`, from `OP;P_2`, is that of `M_1` from `OA, M_2`, is that of `P_2`, from `OP; P_3` is that of `M_2`, from OA and so on. If `P_n` denotes the nth foot of the perpendicular on OA, then find `OP_n`.

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