The hint - world cup medallions

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]=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

Have fun!

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