In a mathematical competition $n=10\,000$ contestants participate. During the final party, in sequence, the first one takes $1/n$ of the cake, the second one takes $2/n$ of the remaining cake, the third one takes $3/n$ of the cake that remains after the first and the second contestant, and so on until the last one, who takes all of the remaining cake. Determine which competitor takes the largest piece of cake.