is the EV for this game really infinity?

[dchz]

just did this in econ class but i didn't think it was true....
i thought i might have missed something so 2p2, analyze this game with me

basically we'll flip coins:

If you get head on the first flip, i will give you 2 dollars

if you get tails on the first flip and get head on the 2nd flip, i will give you 4 dollars

if you get tails on the first 2 flips and get head on the 3rd flip i will give you 8 dollars

if you get tails on the first N-1 flips and get head on the nth flip, i will give you 2^(n) dollars

what is the EV for this game?


the answer i got in class was infinity

because the EV is (1/2)x2 + 1/4 (4)+ 1/8 (8) +.... + 1/(2^n) x 2^n

hence the sum of all the EVs = infinty

there seems to be a flaw in the logic here and i can't point it out and it's bugging the crap out of me

solve this for me 2p2