Not to be nitpicky, but an EROEI of 20 implies that you need to produce a little over 21 barrels of oil to get 20 barrels out.  One barrel of oil will be used to produce the 20 barrels of oil but than 1/20 of a barrel of oil will be used to produce the 1 barrel.  Thus you actually need to produce 20 + 1 + 1/20 +1/40 + ... to get 20 barrels out.  
Actually your sequence should be
                1 + 1/20 + 1/40 ....
not 20 + 1 + 1/20 + 1/40 ....
EROI of 20 is one barrel to produce 20 barrels.
I wish my Greek philosophers knowledge was much better (an arrow does not hit a target because after each unit of time it is one half nearer the target, so the arrow never actually hits the target because of decreasing fractions keep on going to infinity) as this is the same argument put forward. In real life, I would not like to rely on a philosopher's hypothesis to protect me when an arrow is shot at me from a long bow.

However, carrying on with your thought experiment, what happens if I use an electrical generator (powered by coal) to power the pump to get the first bit of oil out of the ground, which is then used to pump more oil out of the ground.