MathDB

Initially, the number

1

is written on the blackboard. At each step, the number on the blackboard is erased and another is written, which is obtained by applying any of the following operations:
Operation A: Multiply the number on the board with

\frac12

. Operation B: Subtract the number on the board from

1

.
For example, if the number

\frac38

is on the board, it can be replaced by

\frac12 \frac38=\frac{3}{16}

or by

1-\frac38=\frac58

.
Give a sequence of steps after which the number on the board is

\frac{2009}{2^{20009}}

Problem Statement