AMC 12 2023a Problem 17

Flora the frog starts at $0$ on the number line and makes a sequence of jumps to the right. In any one jump, independent of previous jumps, Flora leaps a positive integer distance $m$ with probability $\frac{1}{2^m}$. What is the probability that Flora will eventually land at $10$?

$\textbf{(A) } \frac{5}{512} \textbf{(B) } \frac{45}{1024} \textbf{(C) } \frac{127}{1024} \textbf{(D) } \frac{511}{1024} \textbf{(E) } \frac{1}{2}$