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PhilGoetz comments on Exterminating life is rational - Less Wrong
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How would it help if this sequence existed?
If the sequence exists, then the paradox* persists even in the face of bounded utility functions. (Or possibly it already persists, as Vladimir Nesov argued and you agreed, but my cold-virus-addled wits aren't sharp enough to see it.)
* The paradox is that each wager has positive expected utility, but accepting all wagers leads to death almost surely.
Ah. So you don't want the sequence to exist.
In the sense that if it exists, then it's a bullet I will bite.