Brainteaser question

Imagine you have a special dollar. You can play a game with me. I'll toss a coin and if you call it right, you have two dollars; if not, you take home only one dollar. You can keep playing if you call correctly, doubling your money each time. How much would you pay for the special dollar?

 

I think if you take a sum of the expected values it adds up to $2

 

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