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 of `P_(1)` is that of `M_(!)` 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 form `M_(n-1),` then `OP_(n)` is equal to

Options

A. `1/(2n)`
B. `1/(2^(n))`
C. `2^(n)-1`
D. `2^(n)+3`

Answer

B