Problem Solving

shahab03 wrote:can someone please help me with this.. thanks

x(1) = 3
x(n+1) = 2x(n) - 1
x(2) = 2x(1) - 1 = 2*3 - 1 = 5
x(3) = 2x(2) - 1 = 2*5 - 1 = 9
x(4) = 2x(3) - 1 = 2*9 - 1 = 17
...
Generalizing, we get that x(n) = 2^n + 1

So, x(20) = 2^20 + 1 and x(19) = 2^19 + 1
Therefore, x^20 - x^19 = 2^20 + 1 - 2^19 - 1 = 2^19(2 - 1) = [spoiler]2^19[/spoiler]

The correct answer is A.