Question: A display count starts at 1 and at each second t = 0, 1, 2, 3,..., it increments in the following ways: if the display

A display count starts at 1 and at each second t = 0, 1, 2, 3,..., it increments in the following ways: if the display count is at n, then it increases 1 with the probability 1/(1+n) and stays the same with the probability (11/(1+n)) . For example, if the display count is at 5, it increases 1 with probability 1/6 and stays the same with probability 5/6. What is the expected time (in seconds) needed for the first 9 to show up on the display?

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