The payoff for getting x heads followed by a tails is $2x.
The expected return is the sum of the products of the probabilities and the payoffs is the sum for x=0 to infinity of (1/2) * (1/2)x * 2x.
(1/2)x * 2x = 1. So the answer is an infinite sum of 1/2's, or infinity.
This problem is a well known paradox in mathematics. The final result must be finite yet the expected value is infinite.
Michael Shackleford, A.S.A.