Challenge question

An individual tosses a fair coin until a tail appears for the first time. If the tail appears on the $n$th flip, the individual wins $2^n$ pounds. Show that the expected winnings are infinite. Would you be willing to pay £1 million to play this game once? Would you be willing to pay £1 million for each game if you could play for as long as you liked and only had to settle up when you stopped playing?