How much would you have to ante to make the St. Petersburg game fair (recall Example 3.5.5)

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How much would you have to ante to make the St. Petersburg game “fair” (recall Example 3.5.5) if the most you could win was $1000? That is, the payoffs are $2k for 1≤k ≤9, and $1000 for k ≥10.
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