A zero-seeking device operates as follows: If it is in state j at time n, then at time n + 1, its position is 0 with probability 1/j, and its position is k (where k is one of the states 1, 2, . . . ,...

A zero-seeking device operates as follows: If it is in state j at time n, then at time n + 1, its position is 0 with probability 1/j, and its position is k (where k is one of the states 1, 2, . . . , j - 1) with probability 2k/j2. Find the expected time until the device first hits zero starting from state m.