From the definition of utility, I should prefer the maximum of the function (2^n)/n where n>=1 (the offer is not possible in n<1). That function keeps increasing with n, so I would choose n=infinity, or the maximum value if there was one. However, humans do not have well-defined utility functions, and there is probably a rough maximum to the amount of possible total utility (as in, there is probably nothing that I would prefer an infinitesimal chance of happening than some arbitrary small but positive and guaranteed utility).
From the definition of utility, I should prefer the maximum of the function (2^n)/n where n>=1 (the offer is not possible in n<1). That function keeps increasing with n, so I would choose n=infinity, or the maximum value if there was one. However, humans do not have well-defined utility functions, and there is probably a rough maximum to the amount of possible total utility (as in, there is probably nothing that I would prefer an infinitesimal chance of happening than some arbitrary small but positive and guaranteed utility).