The line x + y = 1 meets x - axis at A and y - axis at B. P is the mid - point of AB P1 is the foot of the perpendicular from P to OA; M1 is that from P1 to OP; P2 is that from M1 to OA; M2 is that from P2 to OP; P3 is that from M2 to OA and so on. If Pn denotes the nth foot of the perpendicular on OA from Mn−1, then OPn =

The line x + y = 1 meets x - axis at A and y - axis at B. P is the mid

1.	The line x + y = 1 meets x - axis at A and y - axis at B. P is the mid - point of AB P1 is the foot of the perpendicular from P to OA; M1 is that from P1 to OP; P2 is that from M1 to OA; M2 is that from P2 to OP; P3 is that from M2 to OA and so on. If Pn denotes the nth foot of the perpendicular on OA from Mn−1, then OPn =
Answer» 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 of the perpendicular from P to OA; $M_{1}$ is that from $P_{1}$ to OP; $P_{2}$ is that from $M_{1}$ to OA; $M_{2}$ is that from $P_{2}$ to OP; $P_{3}$ is that from $M_{2}$ to OA and so on. If $P_{n}$ denotes the nth foot of the perpendicular on OA from $M_{n - 1}$ , then $O P_{n}$ =