The St. Petersburg paradox is a coin flip game, where a fair coin is tossed successively, until heads occurs. If the first toss is heads, you win $1. If the first one is tails and the second one is heads, you win $2. If the first heads occurs in the third toss, you win $4 and so forth. The amount of money you win is doubled with each coin flip you survive. In the eighteenth century it was believed that the fair price for participating in such a game would be the expected wealth you gain. Show that the expectation value of the St. Petersburg game is infinite.