AMC 12 2023 A 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 1 / 2^{m}. What is the probability that Flora will eventually land at 10?

Answer Choices
A. \dfrac{5}{512}
B. \dfrac{45}{1024}
C. \dfrac{127}{1024}
D. \dfrac{511}{1024}
E. \dfrac{1}{2}