Consider the following game. A fair coin is flipped until the first tail appears; we win $2 if it appears on the first toss, $4 if it appears on the second toss, and in general  if it first occurs on the k-th toss. Let the random variable X denote our winning. How much should we have to pay in order for this to be a fair game? Note: A fair game is one where the difference between the ante and E(X) is 0

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