Chapter 4.3, Problem 27ES

It is a fact that if n is any nonnegative integer, then

$1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\mathrm{....}+\frac{1}{2^n}=\frac{1-\left(1/2^{n+1}\right)}{1-\left(1/2\right)}.$

(A more general from of the this statement is proved in Section 5.2.) Is the right-hand side of the this equation rational? If so, express it as a ratio of two integers.