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 2m1. What is the probability that Flora will eventually land at 10?
Similarly, for reaching n, the probability is1⋅2n1+21⋅2n−11+21⋅2n−21+⋯+21⋅21=2n1+2n1+2n−11+2n−21+⋯+221=2n−11+2n−11+2n−21+⋯+221=2n−21+2n−21+⋯+221⋮=221+221=21
