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 perpendicular 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 theb nth foot of the perpendicular on OA, then find `OP_(n)`
.

Options

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

Answer

B