Let X[n]= T[n] - T[n-1] where T[n] is the number of medallions collected when you first own n different medallions. Hence X=1, but what do we know about X[n] for other values of n?
It might also help to remember, if X and Y are random variables, the average (or expectation) of X + Y is the same as the expectation of X + the expectation of Y. In symbols we may write this as
We will publish the best explanation in the next issue, along with the answer to the problem itself.