# Minimum sum

Given the following sum: $S = \sum_{i=1}^n a_i b_i \ \ \ where \ a_i \ ,\ b_i > 0$ $$S$$ is minimal when the two equences $$[ a_1,a_2,\cdots,a_n]$$ and $$[b_1,b_2,\cdots,b_n]$$

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