I have a problem with the secretary problem, I wanted to prove that maximum value of the probability function of choosing the best applicant is decreasing as n gets bigger. So, in other words: $$F(n):=\max_{r\in [1,n]}\left(\frac{r-1}{n}\sum_{k=r}^{n}\frac{1}{k-1}\right)$$ is a decreasing function.
2026-03-26 12:32:02.1774528322
Secretary problem
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