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A comment on How many draws of a random number [0,1] are needed to sum to 1. Parent comment
Say f(x) is the expected value of the number of draws to get to value x. Then f(x) = 1 + integral_0^x f(x)
Hence f'(x) = f(x), so f(x) = c exp(x) The constant is of course 1, and f(1) = exp(1).
Say f(x) is the expected value of the number of draws to get to value x. Then f(x) = 1 + integral_0^x f(x)
Hence f'(x) = f(x), so f(x) = c exp(x) The constant is of course 1, and f(1) = exp(1).