Suppose you face a sequence of coin flips. If the first flip comes up tails, you win $2. Every flip

that comes up tails thereafter, you win an additional amount that is double the previous winning amount. So on the second tail, you win an additional $4 (so your winnings are $2 + $4). On the third tail you win an addition $8 (so your winnings are $2 + $4 + $8). And so on. The first time your flip comes up heads, the game is over. What is the expected value of this sequence of coin flips?