Given $$a_1< a_2<\dots < a_n,$$
find a permutation $\sigma$ maximizing the sum >$$\sum_{i=1}^n {a_i \over \sigma(i)}.$$
I can't figure our where to begin. I know that the solution is $\sigma=e$, but I cannot prove it.
2026-05-04 20:46:45.1777927605
Find a permutation $\sigma$ maximizing the sum $\sum_{i=1}^n {a_i \over \sigma(i)}$.
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