A deck of n cards numbered I through n, initially in any arbitrary order, is shuffled in the following manner: At each stage, we randomly choose one of the cards and move it to the front of the deck, leaving the relative positions of the other cards unchanged. This procedure is continued until all but one of the cards has been chosen. At this point, it follows by symmetry that all n! possible orderings are equally likely. Find the expected number of stages that are required.
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