2a= 1+ 1/2+ 1/2? + 1/2? +...+ 1/2 N- 1 power
minus
On the left is 2a-a = a.
Yes, the middle 1/2+ 1/2? + 1/2? The N- 1 power of+...+12 is the same, so the subtraction will cancel it out.
So on the right is 1- 1/2 2009.
So 1/2+ 1/2? + 1/2? The n power of +...+ 1/2 = the n power of1-1/2.