9. The mathematician Qin Jiushao (approximately 1202-1261 AD) of the Southern Song Dynasty in China proposed Qin Jiushao's algorithm for evaluating polynomials in his work "Mathematical Treatise in Nine Sections". Figure 3 provides a flowchart illustrating an example of using Qin Jiushao's algorithm. If the inputs are $n=5, v=1, x=2$, then the result calculated by the flowchart is $($.
(A) $2^{5}+2^{4}+2^{3}+2^{2}+2+1$
(B) $2^{5}+2^{4}+2^{3}+2^{2}+2+5$
(C) $2^{6}+2^{5}+2^{4}+2^{3}+2^{2}+2+1$
(D) $2^{4}+2^{3}+2^{2}+2+1$
9. A.

Substituting $n=5$ gives $i=4 \geqslant 0$, at this point, $v=2 \times 1+1=2+1$.
When $i=3 \geqslant 0$,
$$
v=2(2+1)+1=2^{2}+2+1 \text {; }
$$

When $i=2 \geqslant 0$,
$$
v=2\left(2^{2}+2+1\right)+1=2^{3}+2^{2}+2+1 \text {; }
$$

When $i=1 \geqslant 0$,
$$
\begin{array}{c}
v=2\left(2^{3}+2^{2}+2+1\right)+1 \\
=2^{4}+2^{3}+2^{2}+2+1 ;
\end{array}
$$

When $i=0 \geqslant 0$,
$$
\begin{array}{l}
v=2\left(2^{4}+2^{3}+2^{2}+2+1\right)+1 \\
=2^{5}+2^{4}+2^{3}+2^{2}+2+1 ;
\end{array}
$$

When $i=-1$, output $v$ as
$$
2^{5}+2^{4}+2^{3}+2^{2}+2+1 .
$$